98:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115209:0.475422:0.272331:0.475422:0.272331:0.456985:0.115209:0.456985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.115209:0.497783:0.133931:0.497783:0.133931:0.480882:0.115209:0.480882:0.000000:0.000000:0.000000
Sea el vector :@0.148452:0.497783:0.256899:0.497783:0.256899:0.481394:0.148452:0.481394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.290020:0.500915:0.321181:0.500915:0.321181:0.480981:0.290020:0.480981:0.000000:0.000000:0.000000
=:@0.277350:0.498461:0.287467:0.498461:0.287467:0.482888:0.277350:0.482888:0.000000
3,1  y el vector director :@0.296460:0.497783:0.491603:0.497783:0.491603:0.481394:0.296460:0.481394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.265096:0.497783:0.274420:0.497783:0.274420:0.481422:0.265096:0.481422:0.000000
:@0.266042:0.486631:0.273598:0.486631:0.273598:0.469882:0.266042:0.469882:0.000000
( ):@0.175410:0.520026:0.210441:0.520026:0.210441:0.500092:0.175410:0.500092:0.000000:0.000000:0.000000
=:@0.162742:0.517572:0.172859:0.517572:0.172859:0.501999:0.162742:0.501999:0.000000
2,5.  :@0.181851:0.516894:0.221171:0.518151:0.221171:0.501762:0.181851:0.500505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.150858:0.516894:0.158597:0.516894:0.158597:0.500533:0.150858:0.500533:0.000000
:@0.151801:0.505742:0.159356:0.505742:0.159356:0.488993:0.151801:0.488993:0.000000
Determinemos:@0.224525:0.518151:0.339347:0.518151:0.339347:0.501527:0.224525:0.501527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  la  ecuación  vecto-:@0.339347:0.518151:0.487561:0.518151:0.487561:0.501762:0.339347:0.501762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rial de la recta, :@0.148437:0.538523:0.258247:0.538523:0.258247:0.522134:0.148437:0.522134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
demostramos:@0.258542:0.538523:0.364647:0.538523:0.364647:0.521899:0.258542:0.521899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 además, que los :@0.364647:0.538523:0.491630:0.538523:0.491630:0.522134:0.364647:0.522134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puntos D(5, 6) y E(1, –4) pertenecen a la recta :@0.148437:0.555120:0.491613:0.555120:0.491613:0.538731:0.148437:0.538731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para  = 1,   = – 1:@0.148437:0.571716:0.271442:0.571716:0.271442:0.555327:0.148437:0.555327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t :@0.184813:0.571716:0.193511:0.571716:0.193511:0.555355:0.184813:0.555355:0.000000:0.000000
t:@0.224764:0.571716:0.230145:0.571716:0.230145:0.555355:0.224764:0.555355:0.000000
:@0.152376:0.583236:0.114544:0.583236:0.114544:0.566487:0.152376:0.566487:0.000000
:@0.197763:0.583236:0.159931:0.583236:0.159931:0.566487:0.197763:0.566487:0.000000
:@0.226879:0.583236:0.234434:0.583236:0.234434:0.566487:0.226879:0.566487:0.000000
():@0.162481:0.597520:0.181498:0.597520:0.181498:0.577586:0.162481:0.577586:0.000000:0.000000
=+:@0.184153:0.595064:0.218244:0.595064:0.218244:0.579491:0.184153:0.579491:0.000000:0.000000
xt:@0.152531:0.594387:0.173889:0.594387:0.173889:0.578025:0.152531:0.578025:0.000000:0.000000
utv:@0.196823:0.594387:0.233670:0.594387:0.233670:0.578025:0.196823:0.578025:0.000000:0.000000:0.000000
La ecuación vectorial de la recta es::@0.148442:0.617068:0.405873:0.617068:0.405873:0.600679:0.148442:0.600679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.152376:0.632150:0.159931:0.632150:0.159931:0.615401:0.152376:0.615401:0.000000
3,1:@0.203261:0.643301:0.224399:0.643301:0.224399:0.626912:0.203261:0.626912:0.000000:0.000000:0.000000
2,5:@0.255505:0.643301:0.278215:0.643301:0.278215:0.626912:0.255505:0.626912:0.000000:0.000000:0.000000
() ( ) ( ):@0.162481:0.646434:0.284100:0.646434:0.284100:0.626500:0.162481:0.626500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.184153:0.643978:0.194270:0.643978:0.194270:0.628405:0.184153:0.628405:0.000000
+:@0.229706:0.643978:0.239823:0.643978:0.239823:0.628405:0.229706:0.628405:0.000000
xt:@0.152531:0.643301:0.173889:0.643301:0.173889:0.626939:0.152531:0.626939:0.000000:0.000000
t:@0.241426:0.643301:0.246807:0.643301:0.246807:0.626939:0.241426:0.626939:0.000000
:@0.152376:0.665932:0.159931:0.665932:0.159931:0.649183:0.152376:0.649183:0.000000
32 ,1 5:@0.203261:0.677084:0.273194:0.677084:0.273194:0.660695:0.203261:0.660695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
() (:@0.162481:0.680216:0.202959:0.680216:0.202959:0.660283:0.162481:0.660283:0.000000:0.000000:0.000000:0.000000
):@0.279010:0.680216:0.285147:0.680216:0.285147:0.660283:0.279010:0.660283:0.000000
=:@0.184153:0.677762:0.194270:0.677762:0.194270:0.662189:0.184153:0.662189:0.000000
+:@0.213416:0.677762:0.223533:0.677762:0.223533:0.662189:0.213416:0.662189:0.000000
+:@0.252059:0.677762:0.262176:0.677762:0.262176:0.662189:0.252059:0.662189:0.000000
xt:@0.152531:0.677084:0.173889:0.677084:0.173889:0.660723:0.152531:0.660723:0.000000:0.000000
t:@0.233940:0.677084:0.239321:0.677084:0.239321:0.660723:0.233940:0.660723:0.000000
t:@0.272159:0.677084:0.277539:0.677084:0.277539:0.660723:0.272159:0.660723:0.000000
Comprobamos:@0.148452:0.708352:0.263015:0.708352:0.263015:0.691728:0.148452:0.691728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 si los puntos dados pertene-:@0.263015:0.708352:0.487576:0.708352:0.487576:0.691963:0.263015:0.691963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cen a la recta::@0.148452:0.724948:0.248089:0.724948:0.248089:0.708560:0.148452:0.708560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para  = 1, :@0.148452:0.752443:0.224024:0.752443:0.224024:0.736054:0.148452:0.736054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.183354:0.752443:0.188735:0.752443:0.188735:0.736082:0.183354:0.736082:0.000000
reemplazamos:@0.224024:0.752443:0.336967:0.752443:0.336967:0.735819:0.224024:0.735819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.336967:0.752443:0.341003:0.752443:0.341003:0.736054:0.336967:0.736054:0.000000
:@0.344924:0.740036:0.352480:0.740036:0.352480:0.723288:0.344924:0.723288:0.000000
1:@0.360311:0.751183:0.369304:0.751183:0.369304:0.734794:0.360311:0.734794:0.000000
5,6 , :@0.394661:0.751183:0.431275:0.752446:0.431275:0.736057:0.394661:0.734794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
() ( ):@0.355028:0.754320:0.423987:0.754320:0.423987:0.734387:0.355028:0.734387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.375549:0.751865:0.385666:0.751865:0.385666:0.736292:0.375549:0.736292:0.000000
x:@0.345088:0.751187:0.352552:0.751187:0.352552:0.734826:0.345088:0.734826:0.000000
corresponde al punto D.:@0.148466:0.769042:0.326086:0.769042:0.326086:0.752653:0.148466:0.752653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para  = –1, :@0.148466:0.796537:0.254203:0.796537:0.254203:0.780148:0.148466:0.780148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.190352:0.796537:0.195732:0.796537:0.195732:0.780175:0.190352:0.780175:0.000000
reemplazamos:@0.261187:0.796537:0.374132:0.796537:0.374132:0.779913:0.261187:0.779913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.374132:0.796537:0.378168:0.796537:0.378168:0.780148:0.374132:0.780148:0.000000
:@0.389045:0.784128:0.396600:0.784128:0.396600:0.767380:0.389045:0.767380:0.000000
–1:@0.405955:0.795279:0.424161:0.795279:0.424161:0.778890:0.405955:0.778890:0.000000:0.000000
1,–4 , :@0.448357:0.795279:0.491602:0.796538:0.491602:0.780149:0.448357:0.778890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
() (:@0.399150:0.798412:0.449208:0.798412:0.449208:0.778479:0.399150:0.778479:0.000000:0.000000:0.000000:0.000000
):@0.478821:0.798412:0.484958:0.798412:0.484958:0.778479:0.478821:0.778479:0.000000
=:@0.430403:0.795957:0.440520:0.795957:0.440520:0.780384:0.430403:0.780384:0.000000
x:@0.389199:0.795279:0.396662:0.795279:0.396662:0.778918:0.389199:0.778918:0.000000
 :@0.487566:0.796538:0.491602:0.796538:0.491602:0.780149:0.487566:0.780149:0.000000
corresponde al punto E.:@0.148442:0.813134:0.323282:0.813134:0.323282:0.796745:0.148442:0.796745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115199:0.836853:0.119234:0.836853:0.119234:0.820464:0.115199:0.820464:0.000000
Concluimos que los puntos D y E pertenecen  :@0.148442:0.836853:0.491602:0.836853:0.491602:0.820464:0.148442:0.820464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la recta.:@0.148442:0.853450:0.217010:0.853450:0.217010:0.837061:0.148442:0.837061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.540914:0.488412:0.560945:0.488412:0.560945:0.471512:0.540914:0.471512:0.000000:0.000000:0.000000
Dados los puntos de coordenadas A(3, 2); :@0.574157:0.488412:0.883943:0.488412:0.883943:0.472023:0.574157:0.472023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B(–3, 3) :@0.574157:0.505009:0.633347:0.505009:0.633347:0.488620:0.574157:0.488620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontremos:@0.634987:0.505009:0.736818:0.505009:0.736818:0.488385:0.634987:0.488385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la ecuación vecto-:@0.736818:0.505009:0.879890:0.505009:0.879890:0.488620:0.736818:0.488620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rial de la recta y :@0.574157:0.521605:0.692019:0.521605:0.692019:0.505216:0.574157:0.505216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
graficamos:@0.692019:0.521605:0.776583:0.521605:0.776583:0.504981:0.692019:0.504981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.776583:0.521605:0.779790:0.521605:0.779790:0.505216:0.776583:0.505216:0.000000
 :@0.540914:0.541770:0.544950:0.541770:0.544950:0.525381:0.540914:0.525381:0.000000
Tomamos:@0.574157:0.541770:0.649158:0.541770:0.649158:0.525146:0.574157:0.525146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el punto A(3, 2) como el vector :@0.649158:0.541770:0.883388:0.541770:0.883388:0.525381:0.649158:0.525381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540914:0.575557:0.544950:0.575557:0.544950:0.559168:0.540914:0.559168:0.000000
:@0.578084:0.556861:0.540252:0.556861:0.540252:0.540113:0.578084:0.540113:0.000000
:@0.623471:0.556861:0.585640:0.556861:0.585640:0.540113:0.623471:0.540113:0.000000
:@0.652587:0.556861:0.660142:0.556861:0.660142:0.540113:0.652587:0.540113:0.000000
():@0.588189:0.571145:0.607207:0.571145:0.607207:0.551212:0.588189:0.551212:0.000000:0.000000
=+:@0.609862:0.568691:0.643953:0.568691:0.643953:0.553118:0.609862:0.553118:0.000000:0.000000
xt:@0.578240:0.568013:0.599598:0.568013:0.599598:0.551652:0.578240:0.551652:0.000000:0.000000
utv:@0.622532:0.568013:0.659379:0.568013:0.659379:0.551652:0.622532:0.551652:0.000000:0.000000:0.000000
 :@0.540926:0.599284:0.544961:0.599284:0.544961:0.582895:0.540926:0.582895:0.000000
Tomamos:@0.574169:0.599284:0.649170:0.599284:0.649170:0.582660:0.574169:0.582660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el punto A(3, 2) como el vector:@0.649170:0.599284:0.879882:0.599284:0.879882:0.582895:0.649170:0.582895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.577719:0.607241:0.585274:0.607241:0.585274:0.590493:0.577719:0.590493:0.000000
u:@0.576779:0.618388:0.586104:0.618388:0.586104:0.602027:0.576779:0.602027:0.000000
 :@0.589236:0.620907:0.593272:0.620907:0.593272:0.604518:0.589236:0.604518:0.000000
 :@0.540919:0.648401:0.544955:0.648401:0.544955:0.632013:0.540919:0.632013:0.000000
El vector de dirección es :@0.574162:0.648401:0.755951:0.648401:0.755951:0.632013:0.574162:0.632013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.759295:0.635994:0.766850:0.635994:0.766850:0.619246:0.759295:0.619246:0.000000
   :@0.792741:0.635994:0.871906:0.635994:0.871906:0.619246:0.792741:0.619246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.823884:0.635994:0.831439:0.635994:0.831439:0.619246:0.823884:0.619246:0.000000
:@0.859228:0.635994:0.866783:0.635994:0.866783:0.619246:0.859228:0.619246:0.000000
,:@0.767880:0.647145:0.771087:0.647145:0.771087:0.630756:0.767880:0.630756:0.000000
,:@0.787672:0.647145:0.790878:0.647145:0.790878:0.630756:0.787672:0.630756:0.000000
–:@0.839969:0.647145:0.849183:0.647145:0.849183:0.630756:0.839969:0.630756:0.000000
=:@0.803685:0.647823:0.813802:0.647823:0.813802:0.632250:0.803685:0.632250:0.000000
vesv OB OA:@0.758353:0.647145:0.873121:0.647145:0.873121:0.630784:0.758353:0.630784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540926:0.674640:0.544961:0.674640:0.544961:0.658251:0.540926:0.658251:0.000000
:@0.577510:0.663490:0.585065:0.663490:0.585065:0.646742:0.577510:0.646742:0.000000
–3,3 –3,2:@0.607925:0.674643:0.688251:0.674643:0.688251:0.658254:0.607925:0.658254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–6,1:@0.716685:0.674643:0.747828:0.674643:0.747828:0.658254:0.716685:0.658254:0.000000:0.000000:0.000000:0.000000
(:@0.601119:0.677774:0.607255:0.677774:0.607255:0.657841:0.601119:0.657841:0.000000
) ( ) (:@0.639172:0.677774:0.716042:0.677774:0.716042:0.657841:0.639172:0.657841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.745305:0.677774:0.751441:0.677774:0.751441:0.657841:0.745305:0.657841:0.000000
=:@0.588451:0.675320:0.598567:0.675320:0.598567:0.659747:0.588451:0.659747:0.000000
=:@0.697229:0.675320:0.707346:0.675320:0.707346:0.659747:0.697229:0.659747:0.000000
v:@0.576566:0.674643:0.584306:0.674643:0.584306:0.658281:0.576566:0.658281:0.000000
 :@0.540909:0.698362:0.544945:0.698362:0.544945:0.681973:0.540909:0.681973:0.000000
La ecuación vectorial de la recta es::@0.574152:0.698362:0.831585:0.698362:0.831585:0.681973:0.574152:0.681973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540909:0.724210:0.544945:0.724210:0.544945:0.707821:0.540909:0.707821:0.000000
:@0.578084:0.713454:0.585640:0.713454:0.585640:0.696706:0.578084:0.696706:0.000000
3,2:@0.628970:0.724605:0.651260:0.724605:0.651260:0.708216:0.628970:0.708216:0.000000:0.000000:0.000000
–6,1:@0.685462:0.724605:0.716600:0.724605:0.716600:0.708216:0.685462:0.708216:0.000000:0.000000:0.000000:0.000000
() ( ) (:@0.588189:0.727737:0.684787:0.727737:0.684787:0.707804:0.588189:0.707804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.714050:0.727737:0.720186:0.727737:0.720186:0.707804:0.714050:0.707804:0.000000
=:@0.609862:0.725283:0.619979:0.725283:0.619979:0.709710:0.609862:0.709710:0.000000
+:@0.659285:0.725283:0.669401:0.725283:0.669401:0.709710:0.659285:0.709710:0.000000
xt:@0.578240:0.724605:0.599598:0.724605:0.599598:0.708244:0.578240:0.708244:0.000000:0.000000
t:@0.671005:0.724605:0.676386:0.724605:0.676386:0.708244:0.671005:0.708244:0.000000
 :@0.540906:0.747937:0.544941:0.747937:0.544941:0.731548:0.540906:0.731548:0.000000
La gráfica se muestra en la figura.:@0.574149:0.747937:0.816988:0.747937:0.816988:0.731548:0.574149:0.731548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540906:0.915629:0.544941:0.915629:0.544941:0.899241:0.540906:0.899241:0.000000
A:@0.801275:0.843337:0.809115:0.843337:0.809115:0.831418:0.801275:0.831418:0.000000
B:@0.631111:0.820495:0.637879:0.820495:0.637879:0.808575:0.631111:0.808575:0.000000
1:@0.740604:0.903909:0.747144:0.903909:0.747144:0.891990:0.740604:0.891990:0.000000
–2:@0.652621:0.903909:0.665862:0.903909:0.665862:0.891990:0.652621:0.891990:0.000000:0.000000
–1 0:@0.680952:0.903909:0.711026:0.903909:0.711026:0.891990:0.680952:0.891990:0.000000:0.000000:0.000000:0.000000
3:@0.796651:0.903909:0.803191:0.903909:0.803191:0.891990:0.796651:0.891990:0.000000
y:@0.712139:0.774316:0.718035:0.774316:0.718035:0.762397:0.712139:0.762397:0.000000
x:@0.848262:0.894645:0.854011:0.894645:0.854011:0.882726:0.848262:0.882726:0.000000
2:@0.769258:0.903909:0.775798:0.903909:0.775798:0.891990:0.769258:0.891990:0.000000
4:@0.823830:0.903909:0.830370:0.903909:0.830370:0.891990:0.823830:0.891990:0.000000
1:@0.701216:0.872305:0.707756:0.872305:0.707756:0.860386:0.701216:0.860386:0.000000
3:@0.701216:0.828501:0.707756:0.828501:0.707756:0.816582:0.701216:0.816582:0.000000
–4:@0.595957:0.903909:0.609198:0.903909:0.609198:0.891990:0.595957:0.891990:0.000000:0.000000
2:@0.701216:0.850257:0.707756:0.850257:0.707756:0.838338:0.701216:0.838338:0.000000
4:@0.701216:0.805789:0.707756:0.805789:0.707756:0.793870:0.701216:0.793870:0.000000
–3:@0.624289:0.903899:0.637530:0.903899:0.637530:0.891980:0.624289:0.891980:0.000000:0.000000
Sean  ,:@0.429561:0.181273:0.486604:0.180015:0.486604:0.163626:0.429561:0.164884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.474445:0.168864:0.496024:0.168864:0.496024:0.152116:0.474445:0.152116:0.000000:0.000000
:@0.516276:0.180883:0.529581:0.180883:0.529581:0.164134:0.516276:0.164134:0.000000
∈:@0.499783:0.180689:0.512922:0.180689:0.512922:0.165116:0.499783:0.165116:0.000000
2:@0.530357:0.172354:0.535568:0.172354:0.535568:0.162856:0.530357:0.162856:0.000000
uv:@0.473504:0.180015:0.495267:0.180015:0.495267:0.163654:0.473504:0.163654:0.000000:0.000000
dos vectores definidos en el sistema de coor-:@0.539567:0.181274:0.879889:0.181274:0.879889:0.164885:0.539567:0.164885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denadas rectangulares, se puede definir la ecuación vectorial :@0.429554:0.197870:0.883906:0.197870:0.883906:0.181481:0.429554:0.181481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la recta L que pasa por el extremo del vector   y es paralela :@0.429554:0.216984:0.883936:0.216980:0.883936:0.200591:0.429554:0.200595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.776225:0.216980:0.785549:0.216980:0.785549:0.200619:0.776225:0.200619:0.000000
:@0.777165:0.205833:0.784720:0.205833:0.784720:0.189084:0.777165:0.189084:0.000000
al vector  , también conocido como vector generador o vec-:@0.429566:0.236093:0.879884:0.236091:0.879884:0.219702:0.429566:0.219705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.498403:0.236091:0.506143:0.236091:0.506143:0.219730:0.498403:0.219730:0.000000
:@0.499343:0.224944:0.506898:0.224944:0.506898:0.208195:0.499343:0.208195:0.000000
tor director de la recta L, de la siguiente manera::@0.429567:0.252687:0.781585:0.252687:0.781585:0.236298:0.429567:0.236298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.604313:0.271861:0.611869:0.271861:0.611869:0.255113:0.604313:0.255113:0.000000
:@0.649129:0.269026:0.656685:0.269026:0.656685:0.252277:0.649129:0.252277:0.000000
:@0.678245:0.269026:0.685800:0.269026:0.685800:0.252277:0.678245:0.252277:0.000000
:@0.716136:0.281055:0.729440:0.281055:0.729440:0.264306:0.716136:0.264306:0.000000
{:@0.593320:0.285255:0.602166:0.285255:0.602166:0.261273:0.593320:0.261273:0.000000
}:@0.729482:0.285255:0.738328:0.285255:0.738328:0.261273:0.729482:0.261273:0.000000
():@0.613842:0.283316:0.632859:0.283316:0.632859:0.263383:0.613842:0.263383:0.000000:0.000000
=:@0.581436:0.280861:0.591553:0.280861:0.591553:0.265288:0.581436:0.265288:0.000000
= +:@0.635521:0.280861:0.669609:0.280861:0.669609:0.265288:0.635521:0.265288:0.000000:0.000000:0.000000
∈:@0.699646:0.280861:0.712785:0.280861:0.712785:0.265288:0.699646:0.265288:0.000000
L:@0.571072:0.280183:0.578701:0.280183:0.578701:0.263822:0.571072:0.263822:0.000000
x t:@0.603523:0.280183:0.625249:0.280183:0.625249:0.263822:0.603523:0.263822:0.000000:0.000000:0.000000
u tv t:@0.648191:0.280183:0.695458:0.280183:0.695458:0.263822:0.648191:0.263822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Donde los vectores   y :@0.429566:0.317733:0.603571:0.317739:0.603571:0.301350:0.429566:0.301344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.575369:0.316482:0.583108:0.316482:0.583108:0.300120:0.575369:0.300120:0.000000
:@0.576308:0.305334:0.583864:0.305334:0.583864:0.288586:0.576308:0.288586:0.000000
tv:@0.605111:0.316482:0.618932:0.316482:0.618932:0.300120:0.605111:0.300120:0.000000:0.000000
:@0.612132:0.305334:0.619687:0.305334:0.619687:0.288586:0.612132:0.288586:0.000000
 son colineales, con :@0.624691:0.317739:0.769033:0.317739:0.769033:0.301350:0.624691:0.301350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.796629:0.317353:0.809934:0.317353:0.809934:0.300604:0.796629:0.300604:0.000000
. Además, :@0.809971:0.316482:0.883939:0.317739:0.883939:0.301350:0.809971:0.300093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.780137:0.317159:0.793275:0.317159:0.793275:0.301586:0.780137:0.301586:0.000000
t:@0.770554:0.316482:0.775935:0.316482:0.775935:0.300120:0.770554:0.300120:0.000000
cada elemento de la recta L es de la forma::@0.429551:0.334335:0.741691:0.334335:0.741691:0.317946:0.429551:0.317946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.612219:0.349422:0.619774:0.349422:0.619774:0.332673:0.612219:0.332673:0.000000
:@0.641335:0.349422:0.648890:0.349422:0.648890:0.332673:0.641335:0.332673:0.000000
:@0.683103:0.361445:0.696408:0.361445:0.696408:0.344697:0.683103:0.344697:0.000000
,:@0.649915:0.360574:0.653122:0.360574:0.653122:0.344185:0.649915:0.344185:0.000000
.:@0.654043:0.360574:0.657249:0.360574:0.657249:0.344185:0.654043:0.344185:0.000000
+:@0.622585:0.361251:0.632702:0.361251:0.632702:0.345679:0.622585:0.345679:0.000000
∈:@0.666609:0.361251:0.679748:0.361251:0.679748:0.345679:0.666609:0.345679:0.000000
utvt:@0.611277:0.360574:0.662414:0.360574:0.662414:0.344213:0.611277:0.344213:0.000000:0.000000:0.000000:0.000000
La ecuación vectorial de un segmento de recta está definido :@0.429562:0.389327:0.883894:0.389327:0.883894:0.372938:0.429562:0.372938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la siguiente manera:@0.429562:0.405923:0.596699:0.405923:0.596699:0.389534:0.429562:0.389534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.584159:0.435295:0.603176:0.435295:0.603176:0.415362:0.584159:0.415362:0.000000:0.000000
[:@0.696033:0.435212:0.702169:0.435212:0.702169:0.415591:0.696033:0.415591:0.000000
]:@0.730105:0.435212:0.736242:0.435212:0.736242:0.415591:0.730105:0.415591:0.000000
=+:@0.605833:0.432841:0.639924:0.432841:0.639924:0.417268:0.605833:0.417268:0.000000:0.000000
∈:@0.679912:0.432841:0.693051:0.432841:0.693051:0.417268:0.679912:0.417268:0.000000
,:@0.657135:0.432163:0.660342:0.432163:0.660342:0.415774:0.657135:0.415774:0.000000
...:@0.661263:0.432163:0.670551:0.432163:0.670551:0.415774:0.661263:0.415774:0.000000:0.000000:0.000000
,:@0.715238:0.432163:0.718444:0.432163:0.718444:0.415774:0.715238:0.415774:0.000000
0:@0.707708:0.434167:0.712919:0.434167:0.712919:0.424669:0.707708:0.424669:0.000000
1:@0.724357:0.434167:0.729569:0.434167:0.729569:0.424669:0.724357:0.424669:0.000000
xt:@0.574213:0.432163:0.595570:0.432163:0.595570:0.415802:0.574213:0.415802:0.000000:0.000000
utvt:@0.618494:0.432163:0.675712:0.432163:0.675712:0.415802:0.618494:0.415802:0.000000:0.000000:0.000000:0.000000
tt:@0.702064:0.432163:0.724766:0.432163:0.724766:0.415802:0.702064:0.415802:0.000000:0.000000
:@0.574055:0.421011:0.536223:0.421011:0.536223:0.404263:0.574055:0.404263:0.000000
:@0.619442:0.421011:0.581611:0.421011:0.581611:0.404263:0.619442:0.404263:0.000000
:@0.648558:0.421011:0.656113:0.421011:0.656113:0.404263:0.648558:0.404263:0.000000
Ecuación vectorial de la recta:@0.115891:0.141978:0.552022:0.141978:0.552022:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.2.9. 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 dos puntos de la :@0.125388:0.069719:0.877720:0.069719:0.877720:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta.:@0.125388:0.080280:0.150752:0.080280:0.150752:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.055475:0.122645:0.075035:0.122645:0.075035:0.065614:0.055475:0.065614:0.000000
y:@0.178556:0.159736:0.184453:0.159736:0.184453:0.147817:0.178556:0.147817:0.000000
x:@0.386125:0.252666:0.391875:0.252666:0.391875:0.240747:0.386125:0.240747:0.000000
0:@0.183100:0.254054:0.189640:0.254054:0.189640:0.242135:0.183100:0.242135:0.000000
V:@0.238878:0.213941:0.245700:0.213941:0.245700:0.202022:0.238878:0.202022:0.000000
L:@0.378915:0.208328:0.384919:0.208328:0.384919:0.196409:0.378915:0.196409:0.000000
t  V:@0.282212:0.189713:0.294830:0.190628:0.294830:0.180216:0.282212:0.179301:0.000000:0.000000:0.000000:0.000000
X:@0.288680:0.222063:0.294449:0.222063:0.294449:0.211652:0.288680:0.211652:0.000000
U:@0.206241:0.254791:0.213277:0.254791:0.213277:0.244379:0.206241:0.244379:0.000000
u:@0.334653:0.199801:0.340587:0.199801:0.340587:0.189390:0.334653:0.189390:0.000000
y:@0.181240:0.304941:0.187137:0.304941:0.187137:0.293022:0.181240:0.293022:0.000000
v:@0.217988:0.355132:0.224046:0.355132:0.224046:0.343213:0.217988:0.343213:0.000000
x:@0.385311:0.379232:0.391060:0.379232:0.391060:0.367313:0.385311:0.367313:0.000000
x:@0.364645:0.350495:0.370395:0.350495:0.370395:0.338576:0.364645:0.338576:0.000000
1:@0.370383:0.352804:0.374196:0.352804:0.374196:0.345855:0.370383:0.345855:0.000000
u:@0.236972:0.392487:0.244088:0.392487:0.244088:0.380567:0.236972:0.380567:0.000000
0:@0.182493:0.378857:0.189033:0.378857:0.189033:0.366938:0.182493:0.366938:0.000000
W:@0.292335:0.330507:0.303325:0.330507:0.303325:0.318587:0.292335:0.318587:0.000000
B:@0.382302:0.360823:0.389070:0.360823:0.389070:0.348904:0.382302:0.348904:0.000000
[A, B]:@0.298460:0.392074:0.326242:0.392074:0.326242:0.380155:0.298460:0.380155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.167791:0.437488:0.175631:0.437488:0.175631:0.425569:0.167791:0.425569:0.000000
L = u + W:@0.251206:0.411843:0.296304:0.411843:0.296304:0.401431:0.251206:0.401431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.153684:0.419306:0.159454:0.419306:0.159454:0.408894:0.153684:0.408894:0.000000