52:@0.058599:0.966558:0.074760:0.966558:0.074760:0.950778:0.058599:0.950778:0.000000:0.000000
M.5.2.20. Escribir y reconocer la ecuación vectorial y paramétrica de una recta a partir de un punto de la recta y un vector dirección, o a partir de :@0.158445:0.947218:0.883923:0.947218:0.883923:0.935742:0.158445:0.935742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos puntos de la recta, y graficarlas en  .:@0.158445:0.959288:0.363895:0.959288:0.363895:0.947812:0.158445:0.947812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.348855:0.958614:0.358532:0.958614:0.358532:0.949260:0.348855:0.949260:0.000000
3:@0.358532:0.954869:0.361978:0.954869:0.361978:0.948178:0.358532:0.948178:0.000000
Ecuación vectorial y paramétrica  :@0.404235:0.118449:0.829511:0.118449:0.829511:0.073790:0.404235:0.073790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de una recta en el espacio:@0.404235:0.156168:0.725478:0.156168:0.725478:0.111509:0.404235:0.111509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.178042:0.484320:0.178042:0.484320:0.161096:0.404236:0.161096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean :@0.484322:0.177579:0.532716:0.177579:0.532716:0.161082:0.484322:0.161082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.782951:0.181797:0.797465:0.181797:0.797465:0.159528:0.782951:0.159528:0.000000
(:@0.566113:0.182420:0.572807:0.182420:0.572807:0.159994:0.566113:0.159994:0.000000
):@0.632191:0.182420:0.638885:0.182420:0.638885:0.159994:0.632191:0.159994:0.000000
(:@0.681544:0.182420:0.688238:0.182420:0.688238:0.159994:0.681544:0.159994:0.000000
) (:@0.746818:0.182420:0.773275:0.182420:0.773275:0.159994:0.746818:0.159994:0.000000:0.000000:0.000000
=:@0.552292:0.179247:0.563329:0.179247:0.563329:0.162258:0.552292:0.162258:0.000000
=:@0.667723:0.179247:0.678759:0.179247:0.678759:0.162258:0.667723:0.162258:0.000000
∈:@0.760920:0.179247:0.775253:0.179247:0.775253:0.162258:0.760920:0.162258:0.000000
,,:@0.589322:0.178583:0.614189:0.178583:0.614189:0.161368:0.589322:0.161368:0.000000:0.000000
,:@0.641368:0.178583:0.644243:0.178583:0.644243:0.161368:0.641368:0.161368:0.000000
, ,:@0.704511:0.178583:0.729097:0.178583:0.729097:0.161368:0.704511:0.161368:0.000000:0.000000:0.000000
1:@0.581974:0.180928:0.587099:0.180928:0.587099:0.170976:0.581974:0.170976:0.000000
2:@0.602754:0.180928:0.607879:0.180928:0.607879:0.170976:0.602754:0.170976:0.000000
3:@0.624743:0.180928:0.629868:0.180928:0.629868:0.170976:0.624743:0.170976:0.000000
1:@0.697148:0.180928:0.702273:0.180928:0.702273:0.170976:0.697148:0.170976:0.000000
2:@0.717661:0.180928:0.722786:0.180928:0.722786:0.170976:0.717661:0.170976:0.000000
3:@0.739382:0.180928:0.744507:0.180928:0.744507:0.170976:0.739382:0.170976:0.000000
3:@0.798282:0.170199:0.803408:0.170199:0.803408:0.160247:0.798282:0.160247:0.000000
a:@0.539361:0.178704:0.548729:0.178704:0.548729:0.161519:0.539361:0.161519:0.000000
a aa:@0.573556:0.178704:0.625220:0.178704:0.625220:0.161519:0.573556:0.161519:0.000000:0.000000:0.000000:0.000000
b:@0.654108:0.178704:0.663778:0.178704:0.663778:0.161519:0.654108:0.161519:0.000000
b bba:@0.688565:0.178704:0.749197:0.178704:0.749197:0.161519:0.688565:0.161519:0.000000:0.000000:0.000000:0.000000:0.000000
 con   no :@0.807818:0.177579:0.895905:0.177579:0.895905:0.161082:0.807818:0.161082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.983418:0.181797:0.997933:0.181797:0.997933:0.159528:0.983418:0.159528:0.000000
):@0.832659:0.182420:0.839353:0.182420:0.839353:0.159994:0.832659:0.159994:0.000000
(:@0.882011:0.182420:0.888705:0.182420:0.888705:0.159994:0.882011:0.159994:0.000000
):@0.947285:0.182420:0.953979:0.182420:0.953979:0.159994:0.947285:0.159994:0.000000
=:@0.752760:0.179247:0.763796:0.179247:0.763796:0.162258:0.752760:0.162258:0.000000
=:@0.868190:0.179247:0.879227:0.179247:0.879227:0.162258:0.868190:0.162258:0.000000
∈:@0.961387:0.179247:0.975721:0.179247:0.975721:0.162258:0.961387:0.162258:0.000000
,,:@0.789789:0.178583:0.814657:0.178583:0.814657:0.161368:0.789789:0.161368:0.000000:0.000000
,:@0.841836:0.178583:0.844710:0.178583:0.844710:0.161368:0.841836:0.161368:0.000000
, ,:@0.904979:0.178583:0.929565:0.178583:0.929565:0.161368:0.904979:0.161368:0.000000:0.000000:0.000000
1:@0.782442:0.180928:0.787567:0.180928:0.787567:0.170976:0.782442:0.170976:0.000000
2:@0.803222:0.180928:0.808347:0.180928:0.808347:0.170976:0.803222:0.170976:0.000000
3:@0.825211:0.180928:0.830336:0.180928:0.830336:0.170976:0.825211:0.170976:0.000000
1:@0.897615:0.180928:0.902741:0.180928:0.902741:0.170976:0.897615:0.170976:0.000000
2:@0.918128:0.180928:0.923253:0.180928:0.923253:0.170976:0.918128:0.170976:0.000000
3:@0.939850:0.180928:0.944975:0.180928:0.944975:0.170976:0.939850:0.170976:0.000000
3:@0.998750:0.170199:1.003875:0.170199:1.003875:0.160247:0.998750:0.160247:0.000000
a aa:@0.774024:0.178704:0.825688:0.178704:0.825688:0.161519:0.774024:0.161519:0.000000:0.000000:0.000000:0.000000
b:@0.854576:0.178704:0.864245:0.178704:0.864245:0.161519:0.854576:0.161519:0.000000
b bb:@0.889032:0.178704:0.940475:0.178704:0.940475:0.161519:0.889032:0.161519:0.000000:0.000000:0.000000:0.000000
nulo. El conjunto   definido como :@0.404236:0.201841:0.654548:0.201841:0.654548:0.185344:0.404236:0.185344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.530327:0.201957:0.539902:0.201957:0.539902:0.185488:0.530327:0.185488:0.000000
:@0.691434:0.188446:0.726252:0.188446:0.726252:0.170929:0.691434:0.170929:0.000000:0.000000
:@0.754015:0.188446:0.762257:0.188446:0.762257:0.170929:0.754015:0.170929:0.000000
:@0.796346:0.202512:0.810860:0.202512:0.810860:0.184995:0.796346:0.184995:0.000000
^:@0.680860:0.208287:0.560464:0.208287:0.560464:0.176160:0.680860:0.176160:0.000000
`:@0.811308:0.208287:0.690912:0.208287:0.690912:0.176160:0.811308:0.176160:0.000000
 :@0.728760:0.202361:0.692736:0.202361:0.692736:0.184211:0.728760:0.184211:0.000000
:@0.780425:0.202361:0.744400:0.202361:0.744400:0.184211:0.780425:0.184211:0.000000
=:@0.667457:0.202407:0.678734:0.202407:0.678734:0.185177:0.667457:0.185177:0.000000
=:@0.703360:0.202407:0.714638:0.202407:0.714638:0.185177:0.703360:0.185177:0.000000
|:@0.764493:0.202407:0.769720:0.202407:0.769720:0.185177:0.764493:0.185177:0.000000
,:@0.822952:0.202407:0.825827:0.202407:0.825827:0.185177:0.822952:0.185177:0.000000
R:@0.654892:0.202512:0.664883:0.202512:0.664883:0.185327:0.654892:0.185327:0.000000
x atbt:@0.691640:0.202512:0.777500:0.202512:0.777500:0.185327:0.691640:0.185327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 represen-:@0.821098:0.201845:0.891763:0.201845:0.891763:0.185348:0.821098:0.185348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ta una recta que pasa por   y es paralela al vector  . El vector   se :@0.404236:0.221495:0.895902:0.221497:0.895902:0.204999:0.404236:0.204997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.839365:0.224456:0.853879:0.224456:0.853879:0.202187:0.839365:0.202187:0.000000
(:@0.622525:0.225079:0.629219:0.225079:0.629219:0.202653:0.622525:0.202653:0.000000
) (:@0.688603:0.225079:0.694115:0.225079:0.694115:0.202653:0.688603:0.202653:0.000000:0.000000:0.000000
( ) (:@0.737956:0.225079:0.781041:0.226336:0.781041:0.203911:0.737956:0.202653:0.000000:0.000000:0.000000:0.000000:0.000000
) (:@0.803230:0.225079:0.809545:0.225079:0.809545:0.202653:0.803230:0.202653:0.000000:0.000000:0.000000
=:@0.608704:0.221906:0.619741:0.221906:0.619741:0.204917:0.608704:0.204917:0.000000
=:@0.724135:0.221906:0.735171:0.221906:0.735171:0.204917:0.724135:0.204917:0.000000
∈:@0.817332:0.221906:0.831665:0.221906:0.831665:0.204917:0.817332:0.204917:0.000000
,,:@0.645734:0.221242:0.670601:0.221242:0.670601:0.204027:0.645734:0.204027:0.000000:0.000000
, ,,:@0.697780:0.221242:0.735496:0.221242:0.735496:0.204027:0.697780:0.204027:0.000000:0.000000:0.000000:0.000000
, , ,,:@0.760923:0.221242:0.822423:0.222500:0.822423:0.205285:0.760923:0.204027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.638388:0.223587:0.643513:0.223587:0.643513:0.213635:0.638388:0.213635:0.000000
2:@0.659168:0.223587:0.664293:0.223587:0.664293:0.213635:0.659168:0.213635:0.000000
3:@0.681157:0.223587:0.686282:0.223587:0.686282:0.213635:0.681157:0.213635:0.000000
1:@0.753562:0.223587:0.758687:0.223587:0.758687:0.213635:0.753562:0.213635:0.000000
2 1:@0.774074:0.223587:0.795335:0.224845:0.795335:0.214892:0.774074:0.213635:0.000000:0.000000:0.000000
3 2:@0.795796:0.223587:0.816115:0.224845:0.816115:0.214892:0.795796:0.213635:0.000000:0.000000:0.000000
3:@0.854696:0.212858:0.859821:0.212858:0.859821:0.202906:0.854696:0.202906:0.000000
a:@0.595773:0.221363:0.605141:0.221363:0.605141:0.204178:0.595773:0.204178:0.000000
a aa a:@0.629968:0.221363:0.704233:0.221363:0.704233:0.204178:0.629968:0.204178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
baaa:@0.710520:0.221363:0.756963:0.222620:0.756963:0.205435:0.710520:0.204178:0.000000:0.000000:0.000000:0.000000
b bb b bbb:@0.744977:0.221363:0.872012:0.222620:0.872012:0.205435:0.744977:0.204178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.904260:0.224456:0.918774:0.224456:0.918774:0.202187:0.904260:0.202187:0.000000
) (:@0.868125:0.225079:0.896472:0.226336:0.896472:0.203911:0.868125:0.202653:0.000000:0.000000:0.000000
=:@0.673600:0.221906:0.684636:0.221906:0.684636:0.204917:0.673600:0.204917:0.000000
=:@0.789030:0.221906:0.800067:0.221906:0.800067:0.204917:0.789030:0.204917:0.000000
∈:@0.882227:0.221906:0.896561:0.221906:0.896561:0.204917:0.882227:0.204917:0.000000
,:@0.762675:0.221242:0.765550:0.221242:0.765550:0.204027:0.762675:0.204027:0.000000
, ,,:@0.825819:0.221242:0.852477:0.222500:0.852477:0.205285:0.825819:0.204027:0.000000:0.000000:0.000000:0.000000
1:@0.703283:0.223587:0.708408:0.223587:0.708408:0.213635:0.703283:0.213635:0.000000
2:@0.724063:0.223587:0.729189:0.223587:0.729189:0.213635:0.724063:0.213635:0.000000
3:@0.746052:0.223587:0.751177:0.223587:0.751177:0.213635:0.746052:0.213635:0.000000
1 3:@0.818457:0.223587:0.838104:0.224845:0.838104:0.214892:0.818457:0.213635:0.000000:0.000000:0.000000
2:@0.838970:0.223587:0.844095:0.223587:0.844095:0.213635:0.838970:0.213635:0.000000
3:@0.860691:0.223587:0.865816:0.223587:0.865816:0.213635:0.860691:0.213635:0.000000
3:@0.919591:0.212858:0.924717:0.212858:0.924717:0.202906:0.919591:0.202906:0.000000
a:@0.660670:0.221363:0.670038:0.221363:0.670038:0.204178:0.660670:0.204178:0.000000
b a aa:@0.775417:0.221363:0.833454:0.222620:0.833454:0.205435:0.775417:0.204178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.991187:0.225713:1.005701:0.225713:1.005701:0.203444:0.991187:0.203444:0.000000
):@0.840425:0.226336:0.847119:0.226336:0.847119:0.203911:0.840425:0.203911:0.000000
):@0.955052:0.226336:0.961746:0.226336:0.961746:0.203911:0.955052:0.203911:0.000000
=:@0.760526:0.223163:0.771563:0.223163:0.771563:0.206175:0.760526:0.206175:0.000000
=:@0.875957:0.223163:0.886993:0.223163:0.886993:0.206175:0.875957:0.206175:0.000000
∈:@0.969154:0.223163:0.983487:0.223163:0.983487:0.206175:0.969154:0.206175:0.000000
, ,:@0.912745:0.222500:0.937331:0.222500:0.937331:0.205285:0.912745:0.205285:0.000000:0.000000:0.000000
1:@0.905383:0.224845:0.910509:0.224845:0.910509:0.214892:0.905383:0.214892:0.000000
2:@0.925896:0.224845:0.931022:0.224845:0.931022:0.214892:0.925896:0.214892:0.000000
3:@0.947618:0.224845:0.952743:0.224845:0.952743:0.214892:0.947618:0.214892:0.000000
b bb:@0.896799:0.222620:0.948242:0.222620:0.948242:0.205435:0.896799:0.205435:0.000000:0.000000:0.000000:0.000000
llama vector director de la recta  .:@0.404235:0.238848:0.646935:0.238848:0.646935:0.222350:0.404235:0.222350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.634605:0.238963:0.644180:0.238963:0.644180:0.222494:0.634605:0.222494:0.000000
La ecuación :@0.404235:0.261967:0.494628:0.261967:0.494628:0.245470:0.404235:0.245470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.496584:0.247304:0.532668:0.247304:0.532668:0.229787:0.496584:0.229787:0.000000:0.000000:0.000000
:@0.560431:0.247304:0.568673:0.247304:0.568673:0.229787:0.560431:0.229787:0.000000
:@0.617141:0.261365:0.631655:0.261365:0.631655:0.243848:0.617141:0.243848:0.000000
 :@0.535161:0.261214:0.504424:0.261214:0.504424:0.243064:0.535161:0.243064:0.000000
 :@0.581539:0.261214:0.550801:0.261214:0.550801:0.243064:0.581539:0.243064:0.000000
:@0.601219:0.261214:0.614628:0.261214:0.614628:0.243064:0.601219:0.243064:0.000000
=:@0.508927:0.262029:0.520265:0.262029:0.520265:0.242204:0.508927:0.242204:0.000000
,:@0.569115:0.262029:0.574141:0.262029:0.574141:0.242204:0.569115:0.242204:0.000000
xa tb:@0.496785:0.261365:0.569256:0.261365:0.569256:0.244180:0.496785:0.244180:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.592394:0.261365:0.598304:0.261365:0.598304:0.244180:0.592394:0.244180:0.000000
 se llama :@0.638998:0.261961:0.707118:0.261961:0.707118:0.245463:0.638998:0.245463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación vectorial:@0.708678:0.262423:0.850871:0.262423:0.850871:0.245477:0.708678:0.245477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 de la :@0.850858:0.261961:0.895919:0.261961:0.895919:0.245463:0.850858:0.245463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta   en la que el número real   se llama :@0.404231:0.279311:0.707751:0.279311:0.707751:0.262814:0.404231:0.262814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.444245:0.282391:0.458155:0.282391:0.458155:0.261050:0.444245:0.261050:0.000000
t:@0.637088:0.279427:0.642752:0.279427:0.642752:0.262958:0.637088:0.262958:0.000000
parámetro:@0.707751:0.279774:0.789937:0.279774:0.789937:0.262828:0.707751:0.262828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.789941:0.279311:0.796838:0.279311:0.796838:0.262814:0.789941:0.262814:0.000000:0.000000
Nota que       y los elementos de   son puntos :@0.404231:0.301173:0.755465:0.301166:0.755465:0.284668:0.404231:0.284676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.473952:0.301289:0.483527:0.301289:0.483527:0.284820:0.473952:0.284820:0.000000
:@0.486609:0.300956:0.502657:0.300956:0.502657:0.286309:0.486609:0.286309:0.000000
R:@0.505759:0.304253:0.519669:0.304253:0.519669:0.282912:0.505759:0.282912:0.000000
3:@0.519679:0.294814:0.524632:0.294814:0.524632:0.285196:0.519679:0.285196:0.000000
R:@0.659316:0.301281:0.668891:0.301281:0.668891:0.284813:0.659316:0.284813:0.000000
:@0.754802:0.286510:0.763044:0.286510:0.763044:0.268993:0.754802:0.268993:0.000000
:@0.854582:0.300575:0.869097:0.300575:0.869097:0.283059:0.854582:0.283059:0.000000
:@0.838661:0.300425:0.852070:0.300425:0.852070:0.282274:0.838661:0.282274:0.000000
=( ,, ):@0.767155:0.301239:0.836530:0.301239:0.836530:0.281414:0.767155:0.281414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.869923:0.292527:0.875734:0.292527:0.875734:0.281066:0.869923:0.281066:0.000000
x:@0.755011:0.300575:0.762811:0.300575:0.762811:0.283391:0.755011:0.283391:0.000000
x yz:@0.790071:0.300575:0.828909:0.300575:0.828909:0.283391:0.790071:0.283391:0.000000:0.000000:0.000000:0.000000
 :@0.891771:0.301166:0.895913:0.301166:0.895913:0.284668:0.891771:0.284668:0.000000
que se expresan en la forma :@0.404245:0.322912:0.605605:0.322912:0.605605:0.306414:0.404245:0.306414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.609346:0.308261:0.645430:0.308261:0.645430:0.290745:0.609346:0.290745:0.000000:0.000000:0.000000
:@0.673193:0.308261:0.681435:0.308261:0.681435:0.290745:0.673193:0.290745:0.000000
 :@0.647930:0.322176:0.663570:0.322176:0.663570:0.304025:0.647930:0.304025:0.000000
=:@0.621701:0.322991:0.633039:0.322991:0.633039:0.303165:0.621701:0.303165:0.000000
,:@0.681889:0.322991:0.686914:0.322991:0.686914:0.303165:0.681889:0.303165:0.000000
xa tb:@0.609555:0.322327:0.682026:0.322327:0.682026:0.305142:0.609555:0.305142:0.000000:0.000000:0.000000:0.000000:0.000000
 para algún      . :@0.689355:0.322917:0.822786:0.322917:0.822786:0.306419:0.689355:0.306419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.771984:0.323033:0.777648:0.323033:0.777648:0.306564:0.771984:0.306564:0.000000
:@0.781790:0.322700:0.797838:0.322700:0.797838:0.308053:0.781790:0.308053:0.000000
R:@0.801980:0.321948:0.815889:0.321948:0.815889:0.308501:0.801980:0.308501:0.000000
Tenemos la siguiente equivalencia: :@0.404229:0.340268:0.650767:0.340268:0.650767:0.323770:0.404229:0.323770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x R:@0.408265:0.360762:0.445314:0.360762:0.445314:0.343360:0.408265:0.343360:0.000000:0.000000:0.000000
t:@0.481637:0.360762:0.487622:0.360762:0.487622:0.343360:0.481637:0.343360:0.000000
, tal que  =:@0.522882:0.360640:0.617533:0.360640:0.617533:0.343207:0.522882:0.343207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a tb:@0.594316:0.360762:0.665528:0.360762:0.665528:0.343360:0.594316:0.343360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.631348:0.360610:0.647186:0.360610:0.647186:0.342229:0.631348:0.342229:0.000000
,:@0.666656:0.360640:0.669567:0.360640:0.669567:0.343207:0.666656:0.343207:0.000000
y su negación :@0.404236:0.391314:0.505280:0.391314:0.505280:0.374817:0.404236:0.374817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x R:@0.509260:0.389643:0.547102:0.389643:0.547102:0.372458:0.509260:0.372458:0.000000:0.000000:0.000000
t:@0.584227:0.389643:0.590138:0.389643:0.590138:0.372458:0.584227:0.372458:0.000000
, tal que :@0.624956:0.389522:0.689868:0.389522:0.689868:0.372307:0.624956:0.372307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.695497:0.389643:0.703297:0.389643:0.703297:0.372458:0.695497:0.372458:0.000000
a tb:@0.725470:0.389643:0.770008:0.389643:0.770008:0.372458:0.725470:0.372458:0.000000:0.000000:0.000000:0.000000
+:@0.736255:0.389492:0.751895:0.389492:0.751895:0.371341:0.736255:0.371341:0.000000
.:@0.769445:0.390306:0.774471:0.390306:0.774471:0.370481:0.769445:0.370481:0.000000
  :@0.776670:0.391314:0.784955:0.391314:0.784955:0.374817:0.776670:0.374817:0.000000:0.000000
 :@0.826394:0.391314:0.830536:0.391314:0.830536:0.374817:0.826394:0.374817:0.000000
Ecuación vectorial de la recta que pasa por dos puntos:@0.404236:0.417606:0.839815:0.417606:0.839815:0.399924:0.404236:0.399924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dados los puntos  :@0.404236:0.438714:0.541692:0.438714:0.541692:0.422217:0.404236:0.422217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.547091:0.438300:0.556760:0.438300:0.556760:0.421115:0.547091:0.421115:0.000000
= ( , , ),:@0.559968:0.438964:0.653039:0.438964:0.653039:0.419139:0.559968:0.419139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a a:@0.581961:0.438300:0.634923:0.438300:0.634923:0.421115:0.581961:0.421115:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.590122:0.440978:0.595934:0.440978:0.595934:0.429517:0.590122:0.429517:0.000000
2:@0.611953:0.440978:0.617764:0.440978:0.617764:0.429517:0.611953:0.429517:0.000000
3:@0.634464:0.440978:0.640275:0.440978:0.640275:0.429517:0.634464:0.429517:0.000000
q:@0.662046:0.438300:0.671614:0.438300:0.671614:0.421115:0.662046:0.421115:0.000000
= ( , , ):@0.674931:0.438964:0.762614:0.438964:0.762614:0.419139:0.674931:0.419139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b b b:@0.696502:0.438300:0.749262:0.438300:0.749262:0.421115:0.696502:0.421115:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.704824:0.440978:0.710635:0.440978:0.710635:0.429517:0.704824:0.429517:0.000000
2:@0.726393:0.440978:0.732204:0.440978:0.732204:0.429517:0.726393:0.429517:0.000000
3:@0.748642:0.440978:0.754453:0.440978:0.754453:0.429517:0.748642:0.429517:0.000000
3:@0.795758:0.430252:0.801569:0.430252:0.801569:0.418790:0.795758:0.418790:0.000000
con:@0.809056:0.438179:0.836698:0.438179:0.836698:0.420964:0.809056:0.420964:0.000000:0.000000:0.000000
p:@0.843874:0.438300:0.853544:0.438300:0.853544:0.421115:0.843874:0.421115:0.000000
q:@0.874652:0.438300:0.884221:0.438300:0.884221:0.421115:0.874652:0.421115:0.000000
,:@0.885435:0.438179:0.888310:0.438179:0.888310:0.420964:0.885435:0.420964:0.000000
 :@0.891771:0.438714:0.895913:0.438714:0.895913:0.422217:0.891771:0.422217:0.000000
la :@0.404245:0.456065:0.420042:0.456065:0.420042:0.439568:0.404245:0.439568:0.000000:0.000000:0.000000
ecuación vectorial:@0.420004:0.456528:0.560638:0.456528:0.560638:0.439582:0.420004:0.439582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 de la recta  que pasa por estos dos puntos se :@0.560621:0.456065:0.895969:0.456065:0.895969:0.439568:0.560621:0.439568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R :@0.642419:0.456181:0.656136:0.456181:0.656136:0.439712:0.642419:0.439712:0.000000:0.000000
deduce así: El vector director   de la recta :@0.404245:0.475758:0.709285:0.475760:0.709285:0.459262:0.404245:0.459261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.746037:0.478676:0.760551:0.478676:0.760551:0.456407:0.746037:0.456407:0.000000
(:@0.529199:0.479298:0.535893:0.479298:0.535893:0.456873:0.529199:0.456873:0.000000
):@0.595277:0.479298:0.601971:0.479298:0.601971:0.456873:0.595277:0.456873:0.000000
(:@0.644630:0.479298:0.651324:0.479298:0.651324:0.456873:0.644630:0.456873:0.000000
):@0.709904:0.479298:0.716598:0.479298:0.716598:0.456873:0.709904:0.456873:0.000000
=:@0.515378:0.476126:0.526415:0.476126:0.526415:0.459137:0.515378:0.459137:0.000000
=:@0.630809:0.476126:0.641845:0.476126:0.641845:0.459137:0.630809:0.459137:0.000000
∈:@0.724006:0.476126:0.738339:0.476126:0.738339:0.459137:0.724006:0.459137:0.000000
,,:@0.552408:0.475462:0.577275:0.475462:0.577275:0.458247:0.552408:0.458247:0.000000:0.000000
,:@0.604454:0.475462:0.607329:0.475462:0.607329:0.458247:0.604454:0.458247:0.000000
, ,:@0.667597:0.475462:0.692183:0.475462:0.692183:0.458247:0.667597:0.458247:0.000000:0.000000:0.000000
1:@0.545060:0.477808:0.550185:0.477808:0.550185:0.467856:0.545060:0.467856:0.000000
2:@0.565840:0.477808:0.570966:0.477808:0.570966:0.467856:0.565840:0.467856:0.000000
3:@0.587829:0.477808:0.592954:0.477808:0.592954:0.467856:0.587829:0.467856:0.000000
1:@0.660234:0.477808:0.665359:0.477808:0.665359:0.467856:0.660234:0.467856:0.000000
2:@0.680747:0.477808:0.685872:0.477808:0.685872:0.467856:0.680747:0.467856:0.000000
3:@0.702468:0.477808:0.707593:0.477808:0.707593:0.467856:0.702468:0.467856:0.000000
3:@0.761368:0.467080:0.766494:0.467080:0.766494:0.457127:0.761368:0.457127:0.000000
a:@0.502447:0.475583:0.511815:0.475583:0.511815:0.458398:0.502447:0.458398:0.000000
a aa:@0.536642:0.475583:0.588306:0.475583:0.588306:0.458398:0.536642:0.458398:0.000000:0.000000:0.000000:0.000000
b:@0.617194:0.475583:0.626864:0.475583:0.626864:0.458398:0.617194:0.458398:0.000000
b bb:@0.651651:0.475583:0.703094:0.475583:0.703094:0.458398:0.651651:0.458398:0.000000:0.000000:0.000000:0.000000
R,:@0.709285:0.475875:0.721808:0.475875:0.721808:0.459406:0.709285:0.459406:0.000000:0.000000
b p q:@0.407168:0.497095:0.473276:0.497095:0.473276:0.479911:0.407168:0.479911:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.420047:0.497759:0.431385:0.497759:0.431385:0.477934:0.420047:0.477934:0.000000
= ( , , ) ( , , ) = (:@0.476586:0.497759:0.680492:0.497759:0.680492:0.477934:0.476586:0.477934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a a:@0.498579:0.497095:0.551540:0.497095:0.551540:0.479911:0.498579:0.479911:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.506741:0.499773:0.512552:0.499773:0.512552:0.488312:0.506741:0.488312:0.000000
2:@0.528571:0.499773:0.534382:0.499773:0.534382:0.488312:0.528571:0.488312:0.000000
3:@0.551081:0.499773:0.556892:0.499773:0.556892:0.488312:0.551081:0.488312:0.000000
b b b:@0.589875:0.497095:0.642636:0.497095:0.642636:0.479911:0.589875:0.479911:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.598197:0.499773:0.604008:0.499773:0.604008:0.488312:0.598197:0.488312:0.000000
2:@0.619766:0.499773:0.625577:0.499773:0.625577:0.488312:0.619766:0.488312:0.000000
3:@0.642016:0.499773:0.647827:0.499773:0.647827:0.488312:0.642016:0.488312:0.000000
a:@0.681235:0.497095:0.690603:0.497095:0.690603:0.479911:0.681235:0.479911:0.000000
1:@0.689394:0.499773:0.695205:0.499773:0.695205:0.488312:0.689394:0.488312:0.000000
b a:@0.713946:0.497095:0.744298:0.497095:0.744298:0.479911:0.713946:0.479911:0.000000:0.000000:0.000000
1:@0.722270:0.499773:0.728081:0.499773:0.728081:0.488312:0.722270:0.488312:0.000000
,:@0.728919:0.497759:0.733945:0.497759:0.733945:0.477934:0.728919:0.477934:0.000000
2:@0.744100:0.499773:0.749911:0.499773:0.749911:0.488312:0.744100:0.488312:0.000000
b a:@0.769596:0.497095:0.801884:0.497095:0.801884:0.479911:0.769596:0.479911:0.000000:0.000000:0.000000
2:@0.778914:0.499773:0.784724:0.499773:0.784724:0.488312:0.778914:0.488312:0.000000
,:@0.786506:0.497759:0.791531:0.497759:0.791531:0.477934:0.786506:0.477934:0.000000
3:@0.801425:0.499773:0.807236:0.499773:0.807236:0.488312:0.801425:0.488312:0.000000
b:@0.826187:0.497095:0.835857:0.497095:0.835857:0.479911:0.826187:0.479911:0.000000
3:@0.835244:0.499773:0.841054:0.499773:0.841054:0.488312:0.835244:0.488312:0.000000
),:@0.842521:0.497759:0.853819:0.497759:0.853819:0.477934:0.842521:0.477934:0.000000:0.000000
 es el :@0.856551:0.498768:0.895920:0.498768:0.895920:0.482270:0.856551:0.482270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector director de la recta  . La ecuación vectorial de esta recta está :@0.404241:0.516119:0.895958:0.516119:0.895958:0.499621:0.404241:0.499621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.594962:0.516235:0.604536:0.516235:0.604536:0.499766:0.594962:0.499766:0.000000
definida como: :@0.404241:0.533470:0.515092:0.533470:0.515092:0.516972:0.404241:0.516972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x p tb:@0.429175:0.554805:0.501981:0.554805:0.501981:0.537621:0.429175:0.537621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.441215:0.555469:0.452553:0.555469:0.452553:0.535644:0.441215:0.535644:0.000000
+:@0.468229:0.554655:0.483869:0.554655:0.483869:0.536504:0.468229:0.536504:0.000000
= ( , , ):@0.506027:0.555469:0.594493:0.555469:0.594493:0.535644:0.506027:0.535644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a a:@0.528020:0.554805:0.580981:0.554805:0.580981:0.537621:0.528020:0.537621:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.536181:0.557483:0.541992:0.557483:0.541992:0.546022:0.536181:0.546022:0.000000
2:@0.558011:0.557483:0.563822:0.557483:0.563822:0.546022:0.558011:0.546022:0.000000
3:@0.580523:0.557483:0.586334:0.557483:0.586334:0.546022:0.580523:0.546022:0.000000
+:@0.596061:0.554655:0.611701:0.554655:0.611701:0.536504:0.596061:0.536504:0.000000
t a:@0.613551:0.554805:0.636950:0.554805:0.636950:0.537621:0.613551:0.537621:0.000000:0.000000:0.000000
(:@0.620144:0.555469:0.626839:0.555469:0.626839:0.535644:0.620144:0.535644:0.000000
1:@0.635753:0.557483:0.641564:0.557483:0.641564:0.546022:0.635753:0.546022:0.000000
b a:@0.660307:0.554805:0.690657:0.554805:0.690657:0.537621:0.660307:0.537621:0.000000:0.000000:0.000000
1:@0.668629:0.557483:0.674440:0.557483:0.674440:0.546022:0.668629:0.546022:0.000000
,:@0.675278:0.555469:0.680304:0.555469:0.680304:0.535644:0.675278:0.535644:0.000000
2:@0.690461:0.557483:0.696272:0.557483:0.696272:0.546022:0.690461:0.546022:0.000000
b a:@0.715955:0.554805:0.748243:0.554805:0.748243:0.537621:0.715955:0.537621:0.000000:0.000000:0.000000
2:@0.725274:0.557483:0.731085:0.557483:0.731085:0.546022:0.725274:0.546022:0.000000
,:@0.732865:0.555469:0.737890:0.555469:0.737890:0.535644:0.732865:0.535644:0.000000
3:@0.747784:0.557483:0.753595:0.557483:0.753595:0.546022:0.747784:0.546022:0.000000
b:@0.772548:0.554805:0.782217:0.554805:0.782217:0.537621:0.772548:0.537621:0.000000
3:@0.781604:0.557483:0.787415:0.557483:0.787415:0.546022:0.781604:0.546022:0.000000
),:@0.788881:0.555469:0.800179:0.555469:0.800179:0.535644:0.788881:0.535644:0.000000:0.000000
t:@0.824165:0.554805:0.830075:0.554805:0.830075:0.537621:0.824165:0.537621:0.000000
.:@0.863218:0.555469:0.868244:0.555469:0.868244:0.535644:0.863218:0.535644:0.000000
Analizamos las ecuaciones vectorial y paramétrica de la recta   a tra-:@0.404236:0.580116:0.891763:0.580116:0.891763:0.563618:0.404236:0.563618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.840689:0.580231:0.850264:0.580231:0.850264:0.563762:0.840689:0.563762:0.000000
vés de ejemplos.:@0.404236:0.597466:0.519997:0.597466:0.519997:0.580969:0.404236:0.580969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos resueltos:@0.404236:0.622741:0.534585:0.622741:0.534585:0.605954:0.404236:0.605954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404236:0.645586:0.416508:0.645586:0.416508:0.628871:0.404236:0.628871:0.000000:0.000000
  Sean :@0.416508:0.645369:0.465769:0.645369:0.465769:0.628871:0.416508:0.628871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.469772:0.645650:0.477893:0.645650:0.477893:0.628466:0.469772:0.628466:0.000000
=(2, 1, 3) y =:@0.481394:0.645530:0.598172:0.645530:0.598172:0.628315:0.481394:0.628315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.574430:0.645650:0.584422:0.645650:0.584422:0.628466:0.574430:0.628466:0.000000
x t:@0.610978:0.645650:0.642258:0.645650:0.642258:0.628466:0.610978:0.628466:0.000000:0.000000:0.000000
= (2, 1, 3)|:@0.622637:0.645530:0.706788:0.645530:0.706788:0.628315:0.622637:0.628315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.708577:0.645650:0.714487:0.645650:0.714487:0.628466:0.708577:0.628466:0.000000
{:@0.600231:0.651425:0.610282:0.651425:0.610282:0.619299:0.600231:0.619299:0.000000
}:@0.748067:0.651425:0.758119:0.651425:0.758119:0.619299:0.748067:0.619299:0.000000
.:@0.758698:0.645530:0.761573:0.645530:0.761573:0.628315:0.758698:0.628315:0.000000
 Sea     :@0.764823:0.645369:0.831385:0.645369:0.831385:0.628872:0.764823:0.628872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.798921:0.645485:0.808496:0.645485:0.808496:0.629016:0.798921:0.629016:0.000000
⊂:@0.813506:0.644863:0.827243:0.644863:0.827243:0.627151:0.813506:0.627151:0.000000
R:@0.832232:0.644401:0.846142:0.644401:0.846142:0.630954:0.832232:0.630954:0.000000
3:@0.846139:0.639016:0.851092:0.639016:0.851092:0.629398:0.846139:0.629398:0.000000
 la re-:@0.851093:0.645369:0.891762:0.645369:0.891762:0.628872:0.851093:0.628872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presentación de una recta que pasa por el origen :@0.427989:0.667116:0.787321:0.667116:0.787321:0.650618:0.427989:0.650618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 =(0, 0, 0):@0.791674:0.664370:0.876086:0.664370:0.876086:0.647155:0.791674:0.647155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.878786:0.667121:0.895913:0.667121:0.895913:0.650623:0.878786:0.650623:0.000000:0.000000:0.000000
es paralela al vector  . La ecuación vectorial de la recta   está de-:@0.427979:0.689894:0.891724:0.689892:0.891724:0.673394:0.427979:0.673396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.573645:0.690410:0.581766:0.690410:0.581766:0.673226:0.573645:0.673226:0.000000
=(2, 1, 3) y =:@0.585266:0.690290:0.702044:0.690290:0.702044:0.673075:0.585266:0.673075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.678302:0.690410:0.688293:0.690410:0.688293:0.673226:0.678302:0.673226:0.000000
x t:@0.714849:0.690410:0.746131:0.690410:0.746131:0.673226:0.714849:0.673226:0.000000:0.000000:0.000000
= (2, 1, 3)|:@0.726510:0.690290:0.810661:0.690290:0.810661:0.673075:0.726510:0.673075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.812450:0.690410:0.818360:0.690410:0.818360:0.673226:0.812450:0.673226:0.000000
{:@0.704104:0.696185:0.714156:0.696185:0.714156:0.664059:0.704104:0.664059:0.000000
}:@0.851941:0.696185:0.861992:0.696185:0.861992:0.664059:0.851941:0.664059:0.000000
.:@0.862572:0.690290:0.865446:0.690290:0.865446:0.673075:0.862572:0.673075:0.000000
R:@0.822581:0.690007:0.832155:0.690007:0.832155:0.673539:0.822581:0.673539:0.000000
finida como :@0.427976:0.709122:0.516230:0.709122:0.516230:0.692624:0.427976:0.692624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x t:@0.520019:0.709013:0.551262:0.709013:0.551262:0.691829:0.520019:0.691829:0.000000:0.000000:0.000000
= (2, 1, 3),:@0.531642:0.708893:0.611450:0.708893:0.611450:0.691678:0.531642:0.691678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.635925:0.709013:0.641835:0.709013:0.641835:0.691829:0.635925:0.691829:0.000000
.:@0.675816:0.708893:0.678691:0.708893:0.678691:0.691678:0.675816:0.691678:0.000000
 Algunos elementos de  son::@0.681696:0.709128:0.885715:0.709128:0.885715:0.692631:0.681696:0.692631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R :@0.844503:0.709244:0.858027:0.709244:0.858027:0.692775:0.844503:0.692775:0.000000:0.000000
   De la ecuación vectorial :@0.404238:0.833172:0.615054:0.833172:0.615054:0.816674:0.404238:0.816674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x t:@0.623508:0.833623:0.655638:0.833623:0.655638:0.815950:0.623508:0.815950:0.000000:0.000000:0.000000
= (2,1,3),:@0.635461:0.833499:0.705687:0.833499:0.705687:0.815795:0.635461:0.815795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.727088:0.833623:0.733166:0.833623:0.733166:0.815950:0.727088:0.815950:0.000000
, se obtienen las :@0.766838:0.833171:0.895914:0.833171:0.895914:0.816674:0.766838:0.816674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones paramétricas. :@0.427982:0.850522:0.609690:0.850522:0.609690:0.834024:0.427982:0.834024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404247:0.868711:0.408389:0.868711:0.408389:0.852214:0.404247:0.852214:0.000000
Para el efecto, sea  :@0.427982:0.868711:0.560120:0.868711:0.560120:0.852214:0.427982:0.852214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.564096:0.869016:0.571896:0.869016:0.571896:0.851831:0.564096:0.851831:0.000000
=( , , ):@0.575719:0.868896:0.640370:0.868896:0.640370:0.851681:0.575719:0.851681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.596445:0.869016:0.634077:0.869016:0.634077:0.851831:0.596445:0.851831:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.658224:0.869016:0.668215:0.869016:0.668215:0.851831:0.658224:0.851831:0.000000
, existe:@0.668999:0.868896:0.717086:0.868896:0.717086:0.851681:0.668999:0.851681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.723800:0.869016:0.729710:0.869016:0.729710:0.851831:0.723800:0.851831:0.000000
,:@0.764550:0.868896:0.767425:0.868896:0.767425:0.851681:0.764550:0.851681:0.000000
x:@0.564104:0.896280:0.571904:0.896280:0.571904:0.879095:0.564104:0.879095:0.000000
=( , , )= (2,1,3)=(2 , ,3 ),:@0.575719:0.896163:0.787764:0.896163:0.787764:0.878948:0.575719:0.878948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.596445:0.896283:0.634077:0.896283:0.634077:0.879099:0.596445:0.879099:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.656975:0.896283:0.662885:0.896283:0.662885:0.879099:0.656975:0.879099:0.000000
t t t:@0.740603:0.896283:0.778758:0.896283:0.778758:0.879099:0.740603:0.879099:0.000000:0.000000:0.000000:0.000000:0.000000
  tal que :@0.763078:0.868084:0.824649:0.868706:0.824649:0.852208:0.763078:0.851586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.531259:0.893835:0.535401:0.893835:0.535401:0.877338:0.531259:0.877338:0.000000
x:@0.539386:0.861290:0.547186:0.861290:0.547186:0.844105:0.539386:0.844105:0.000000
=( , , ):@0.551009:0.861169:0.615660:0.861169:0.615660:0.843954:0.551009:0.843954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.571735:0.861290:0.609368:0.861290:0.609368:0.844105:0.571735:0.844105:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.633515:0.861290:0.643506:0.861290:0.643506:0.844105:0.633515:0.844105:0.000000
, existe:@0.644290:0.861169:0.692376:0.861169:0.692376:0.843954:0.644290:0.843954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.699090:0.861290:0.705000:0.861290:0.705000:0.844105:0.699090:0.844105:0.000000
,:@0.739840:0.861169:0.742715:0.861169:0.742715:0.843954:0.739840:0.843954:0.000000
x:@0.539395:0.888553:0.547194:0.888553:0.547194:0.871369:0.539395:0.871369:0.000000
=( , , )= (2,1,3)=(2 , ,3 ),:@0.551009:0.888438:0.763054:0.888438:0.763054:0.871223:0.551009:0.871223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.571735:0.888558:0.609368:0.888558:0.609368:0.871374:0.571735:0.871374:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.632265:0.888558:0.638175:0.888558:0.638175:0.871374:0.632265:0.871374:0.000000
t t t:@0.715893:0.888558:0.754048:0.888558:0.754048:0.871374:0.715893:0.871374:0.000000:0.000000:0.000000:0.000000:0.000000
y de la definición de la igualdad de elementos de  , resulta :@0.404236:0.912706:0.830977:0.912706:0.830977:0.896208:0.404236:0.896208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.753858:0.911737:0.767768:0.911737:0.767768:0.898290:0.753858:0.898290:0.000000
3:@0.767765:0.903838:0.772718:0.903838:0.772718:0.894220:0.767765:0.894220:0.000000
x:@0.840400:0.894133:0.848357:0.894133:0.848357:0.876602:0.840400:0.876602:0.000000
=2 ,:@0.852213:0.894010:0.886420:0.894010:0.886420:0.876448:0.852213:0.876448:0.000000:0.000000:0.000000:0.000000
t:@0.875510:0.894133:0.881539:0.894133:0.881539:0.876602:0.875510:0.876602:0.000000
y t:@0.840851:0.912572:0.872679:0.912572:0.872679:0.895041:0.840851:0.895041:0.000000:0.000000:0.000000
= ,:@0.852664:0.912449:0.877560:0.912449:0.877560:0.894887:0.852664:0.894887:0.000000:0.000000:0.000000
z:@0.840422:0.931350:0.847497:0.931350:0.847497:0.913819:0.840422:0.913819:0.000000
=3 .:@0.850962:0.931227:0.883939:0.931227:0.883939:0.913665:0.850962:0.913665:0.000000:0.000000:0.000000:0.000000
t:@0.873808:0.931350:0.879837:0.931350:0.879837:0.913819:0.873808:0.913819:0.000000
para  = 1, = 1(2, 1, 3)=( 2,  1,  3),:@0.430475:0.727366:0.756981:0.727366:0.756981:0.710151:0.430475:0.710151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.471003:0.727487:0.476913:0.727487:0.476913:0.710302:0.471003:0.710302:0.000000
x:@0.524698:0.727487:0.532498:0.727487:0.532498:0.710302:0.524698:0.710302:0.000000
para  =0,:@0.430470:0.754313:0.506319:0.754313:0.506319:0.737098:0.430470:0.737098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.470998:0.754433:0.476908:0.754433:0.476908:0.737249:0.470998:0.737249:0.000000
x:@0.514963:0.754433:0.522763:0.754433:0.522763:0.737249:0.514963:0.737249:0.000000
=0(2, 1, 3)=(0, 0, 0)= 0,:@0.526592:0.754320:0.710906:0.754320:0.710906:0.737105:0.526592:0.737105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si  = 3:@0.430470:0.776952:0.495984:0.776952:0.495984:0.759737:0.430470:0.759737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.449186:0.777072:0.455096:0.777072:0.455096:0.759888:0.449186:0.759888:0.000000
s:@0.496647:0.777072:0.503301:0.777072:0.503301:0.759888:0.496647:0.759888:0.000000
+:@0.504910:0.776921:0.520550:0.776921:0.520550:0.758771:0.504910:0.758771:0.000000
5,:@0.521977:0.776952:0.533637:0.776952:0.533637:0.759737:0.521977:0.759737:0.000000:0.000000
s:@0.558107:0.777072:0.564761:0.777072:0.564761:0.759888:0.558107:0.759888:0.000000
,:@0.598837:0.776952:0.601712:0.776952:0.601712:0.759737:0.598837:0.759737:0.000000
x:@0.436225:0.804019:0.444025:0.804019:0.444025:0.786834:0.436225:0.786834:0.000000
=( 3:@0.447856:0.803906:0.490854:0.803906:0.490854:0.786691:0.447856:0.786691:0.000000:0.000000:0.000000:0.000000
s:@0.491518:0.804026:0.498172:0.804026:0.498172:0.786842:0.491518:0.786842:0.000000
+:@0.499780:0.803876:0.515420:0.803876:0.515420:0.785725:0.499780:0.785725:0.000000
5)(2, 1, 3)=(2( 3:@0.516847:0.803906:0.649059:0.803906:0.649059:0.786691:0.516847:0.786691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s:@0.649722:0.804026:0.656377:0.804026:0.656377:0.786842:0.649722:0.786842:0.000000
+:@0.657985:0.803876:0.673625:0.803876:0.673625:0.785725:0.657985:0.785725:0.000000
5),  3:@0.675052:0.803906:0.726172:0.803906:0.726172:0.786691:0.675052:0.786691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s:@0.726835:0.804026:0.733489:0.804026:0.733489:0.786842:0.726835:0.786842:0.000000
+:@0.735098:0.803876:0.750738:0.803876:0.750738:0.785725:0.735098:0.785725:0.000000
5, 3( 3:@0.752165:0.803906:0.808731:0.803906:0.808731:0.786691:0.752165:0.786691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s:@0.809395:0.804026:0.816049:0.804026:0.816049:0.786842:0.809395:0.786842:0.000000
+:@0.817657:0.803876:0.833297:0.803876:0.833297:0.785725:0.817657:0.785725:0.000000
5)).:@0.834724:0.803906:0.858848:0.803906:0.858848:0.786691:0.834724:0.786691:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.099365:0.307805:0.099365:0.307805:0.083893:0.199646:0.083893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Por dos puntos, cuántas :@0.199884:0.127993:0.364681:0.127993:0.364681:0.112930:0.199884:0.112930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectas pueden pasar?:@0.153341:0.143835:0.288995:0.143835:0.288995:0.128772:0.153341:0.128772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.200167:0.363493:0.200167:0.363493:0.184694:0.199646:0.184694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué son puntos  :@0.199884:0.228794:0.318581:0.228794:0.318581:0.213731:0.199884:0.213731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
colineales:@0.153341:0.244834:0.219074:0.244834:0.219074:0.229573:0.153341:0.229573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.219074:0.244636:0.224281:0.244636:0.224281:0.229573:0.219074:0.229573:0.000000
Recuerda la definición:@0.199646:0.301635:0.355597:0.301635:0.355597:0.286162:0.199646:0.286162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ecuación:@0.199884:0.330263:0.277209:0.330263:0.277209:0.315200:0.199884:0.315200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x u tv:@0.157036:0.350064:0.221187:0.350064:0.221187:0.334125:0.157036:0.334125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.168205:0.350680:0.178722:0.350680:0.178722:0.332291:0.168205:0.332291:0.000000
+:@0.191707:0.349924:0.206214:0.349924:0.206214:0.333089:0.191707:0.333089:0.000000
,:@0.225600:0.349953:0.228267:0.349953:0.228267:0.333985:0.225600:0.333985:0.000000
t:@0.250171:0.350064:0.255653:0.350064:0.255653:0.334125:0.250171:0.334125:0.000000
x a tc:@0.165486:0.372150:0.229164:0.372150:0.229164:0.356210:0.165486:0.356210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.176655:0.372766:0.187172:0.372766:0.187172:0.354377:0.176655:0.354377:0.000000
+:@0.200541:0.372010:0.215048:0.372010:0.215048:0.355175:0.200541:0.355175:0.000000
,:@0.229499:0.372766:0.234161:0.372766:0.234161:0.354377:0.229499:0.354377:0.000000
y b td:@0.165896:0.393142:0.231494:0.393142:0.231494:0.377202:0.165896:0.377202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.177065:0.393758:0.187582:0.393758:0.187582:0.375369:0.177065:0.375369:0.000000
+:@0.200952:0.393002:0.215458:0.393002:0.215458:0.376167:0.200952:0.376167:0.000000
.:@0.232240:0.393030:0.234907:0.393030:0.234907:0.377062:0.232240:0.377062:0.000000
 se conoce :@0.286025:0.350331:0.358707:0.350331:0.358707:0.335268:0.286025:0.335268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como ecuación vectorial de la :@0.153343:0.366173:0.351704:0.366173:0.351704:0.351110:0.153343:0.351110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta  . El vector:@0.153343:0.386451:0.261414:0.386451:0.261414:0.371388:0.153343:0.371388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.189878:0.386557:0.198620:0.386557:0.198620:0.371520:0.189878:0.371520:0.000000
   :@0.261417:0.386774:0.282320:0.386774:0.282320:0.370276:0.261417:0.370276:0.000000:0.000000:0.000000
v:@0.268386:0.387375:0.275695:0.387375:0.275695:0.371909:0.268386:0.371909:0.000000
=(2, 1, 3) y =:@0.278844:0.387266:0.383944:0.387266:0.383944:0.371773:0.278844:0.371773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.362577:0.387375:0.371569:0.387375:0.371569:0.371909:0.362577:0.371909:0.000000
x t:@0.395469:0.387375:0.423623:0.387375:0.423623:0.371909:0.395469:0.371909:0.000000:0.000000:0.000000
= (2, 1, 3)|:@0.405965:0.387266:0.481701:0.387266:0.481701:0.371773:0.405965:0.371773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.483311:0.387375:0.488630:0.387375:0.488630:0.371909:0.483311:0.371909:0.000000
{:@0.385798:0.392572:0.394845:0.392572:0.394845:0.363659:0.385798:0.363659:0.000000
}:@0.518851:0.392572:0.527898:0.392572:0.527898:0.363659:0.518851:0.363659:0.000000
.:@0.528418:0.387266:0.531006:0.387266:0.531006:0.371773:0.528418:0.371773:0.000000
se llama :@0.282321:0.386453:0.337887:0.386453:0.337887:0.371390:0.282321:0.371390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector director de la recta :@0.153351:0.402295:0.325202:0.402295:0.325202:0.387232:0.153351:0.387232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R.:@0.325202:0.402401:0.336635:0.402401:0.336635:0.387364:0.325202:0.387364:0.000000:0.000000
Las ecuaciones paramétricas de :@0.153351:0.418137:0.361034:0.418137:0.361034:0.403074:0.153351:0.403074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la recta   para :@0.153351:0.435484:0.249127:0.435484:0.249127:0.420421:0.153351:0.420421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.204307:0.435590:0.213049:0.435590:0.213049:0.420553:0.204307:0.420553:0.000000
R:@0.249127:0.434600:0.261827:0.434600:0.261827:0.422322:0.249127:0.422322:0.000000
2:@0.261821:0.429456:0.266774:0.429456:0.266774:0.419838:0.261821:0.419838:0.000000
 son::@0.266774:0.435488:0.296537:0.435488:0.296537:0.420425:0.266774:0.420425:0.000000:0.000000:0.000000:0.000000:0.000000
x u tv:@0.157036:0.430498:0.221187:0.430498:0.221187:0.414558:0.157036:0.414558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.168205:0.431114:0.178722:0.431114:0.178722:0.412725:0.168205:0.412725:0.000000
+:@0.191707:0.430358:0.206214:0.430358:0.206214:0.413522:0.191707:0.413522:0.000000
,:@0.225600:0.430386:0.228267:0.430386:0.228267:0.414418:0.225600:0.414418:0.000000
t:@0.250171:0.430498:0.255653:0.430498:0.255653:0.414558:0.250171:0.414558:0.000000
x a tc:@0.165486:0.452583:0.229163:0.452583:0.229163:0.436644:0.165486:0.436644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.176655:0.453199:0.187172:0.453199:0.187172:0.434811:0.176655:0.434811:0.000000
+:@0.200540:0.452444:0.215047:0.452444:0.215047:0.435608:0.200540:0.435608:0.000000
,:@0.229499:0.453199:0.234160:0.453199:0.234160:0.434811:0.229499:0.434811:0.000000
y b td:@0.165896:0.473575:0.231493:0.473575:0.231493:0.457636:0.165896:0.457636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.177065:0.474191:0.187582:0.474191:0.187582:0.455802:0.177065:0.455802:0.000000
+:@0.200950:0.473435:0.215457:0.473435:0.215457:0.456600:0.200950:0.456600:0.000000
.:@0.232239:0.473463:0.234906:0.473463:0.234906:0.457496:0.232239:0.457496:0.000000
 :@0.286025:0.473561:0.289806:0.473561:0.289806:0.458497:0.286025:0.458497:0.000000
Siendo  :@0.153343:0.505878:0.205427:0.505878:0.205427:0.490815:0.153343:0.490815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u (a,b), v (c,d).:@0.207732:0.506354:0.341328:0.506354:0.341328:0.489139:0.207732:0.489139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.221241:0.506927:0.232278:0.506927:0.232278:0.487268:0.221241:0.487268:0.000000
=:@0.290286:0.506927:0.301323:0.506927:0.301323:0.487268:0.290286:0.487268:0.000000
Glosario:@0.199646:0.578463:0.267111:0.578463:0.267111:0.560780:0.199646:0.560780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
colineales::@0.199884:0.605276:0.267130:0.605276:0.267130:0.590015:0.199884:0.590015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 dicho de un :@0.266954:0.605078:0.351015:0.605078:0.351015:0.590015:0.266954:0.590015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto: que se encuentra en la :@0.153341:0.620920:0.344368:0.620920:0.344368:0.605857:0.153341:0.605857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
misma recta que otro.:@0.153341:0.636762:0.291858:0.636762:0.291858:0.621699:0.153341:0.621699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.146910:0.582195:0.158315:0.580685:0.153112:0.558540:0.141707:0.560050:0.000000
c:@0.150292:0.593164:0.160891:0.591761:0.155808:0.570126:0.145209:0.571529:0.000000
b:@0.160667:0.585946:0.173381:0.584263:0.168249:0.562421:0.155535:0.564103:0.000000
Interculturalidad:@0.199646:0.718300:0.319960:0.718300:0.319960:0.702828:0.199646:0.702828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El año chino ordinario :@0.193074:0.746231:0.343664:0.746231:0.343664:0.731168:0.193074:0.731168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consta de 12 meses lunares, :@0.153338:0.762073:0.340512:0.762073:0.340512:0.747010:0.153338:0.747010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su duración oscila entre 353 y :@0.153338:0.777915:0.353776:0.777915:0.353776:0.762852:0.153338:0.762852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
355 días.:@0.153338:0.793757:0.209820:0.793757:0.209820:0.778694:0.153338:0.778694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga responde:@0.153338:0.815580:0.279371:0.815580:0.279371:0.800319:0.153338:0.800319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.199793:0.815382:0.214850:0.815382:0.214850:0.800319:0.199793:0.800319:0.000000:0.000000:0.000000
; ¿cuando :@0.279546:0.815382:0.345632:0.815382:0.345632:0.800319:0.279546:0.800319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se celebra el año chino?, ¿por :@0.153338:0.831224:0.348904:0.831224:0.348904:0.816161:0.153338:0.816161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
qué?:@0.153338:0.847066:0.183734:0.847066:0.183734:0.832003:0.153338:0.832003:0.000000:0.000000:0.000000:0.000000