141:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.º BG:@0.837761:0.967458:0.879897:0.967458:0.879897:0.954794:0.837761:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.096359:0.721252:0.110585:0.721252:0.110585:0.704351:0.096359:0.704351:0.000000:0.000000
  Comprobemos mediante el teorema de Pitágoras si los vectores:@0.110585:0.721252:0.593513:0.721252:0.593513:0.704863:0.110585:0.704863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.744196:0.100395:0.744196:0.100395:0.727808:0.096359:0.727808:0.000000
A:@0.126089:0.743927:0.135985:0.743927:0.135985:0.727566:0.126089:0.727566:0.000000
B:@0.206342:0.743927:0.215187:0.743927:0.215187:0.727566:0.206342:0.727566:0.000000
:@0.126661:0.732628:0.053540:0.732628:0.053540:0.716571:0.126661:0.716571:0.000000
:@0.207337:0.732628:0.134216:0.732628:0.134216:0.716571:0.207337:0.716571:0.000000
=:@0.139118:0.744605:0.149235:0.744605:0.149235:0.729032:0.139118:0.729032:0.000000
= −:@0.219112:0.744605:0.247767:0.744605:0.247767:0.729032:0.219112:0.729032:0.000000:0.000000:0.000000
(, ) y:@0.151851:0.743927:0.201747:0.743927:0.201747:0.727538:0.151851:0.727538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( 3:@0.231841:0.743927:0.256699:0.743927:0.256699:0.727538:0.231841:0.727538:0.000000:0.000000:0.000000
,):@0.256331:0.743927:0.280526:0.743927:0.280526:0.727538:0.256331:0.727538:0.000000:0.000000
2:@0.157080:0.743927:0.166072:0.743927:0.166072:0.727538:0.157080:0.727538:0.000000
2:@0.266704:0.743927:0.275697:0.743927:0.275697:0.727538:0.266704:0.727538:0.000000
 3:@0.171433:0.743927:0.184461:0.743927:0.184461:0.727538:0.171433:0.727538:0.000000:0.000000
 son perpendiculares.:@0.280372:0.744198:0.436856:0.744198:0.436856:0.727809:0.280372:0.727809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso único. :@0.102121:0.514220:0.189100:0.514220:0.189100:0.498642:0.102121:0.498642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hallamos el ángulo entre los vectores dirección de los dos aviones.:@0.189100:0.514220:0.632125:0.514220:0.632125:0.499321:0.189100:0.499321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.111700:0.549266:0.120805:0.549266:0.120805:0.535250:0.111700:0.535250:0.000000
⋅:@0.189765:0.541374:0.193911:0.541374:0.193911:0.527359:0.189765:0.527359:0.000000
⎛:@0.158817:0.535399:0.165186:0.535399:0.165186:0.521383:0.158817:0.521383:0.000000
⎝:@0.158817:0.567401:0.165186:0.567401:0.165186:0.553386:0.158817:0.553386:0.000000
⎜:@0.158817:0.546676:0.165186:0.546676:0.165186:0.532661:0.158817:0.532661:0.000000
⎜:@0.158817:0.558526:0.165186:0.558526:0.165186:0.544511:0.158817:0.544511:0.000000
⎞:@0.216914:0.535399:0.223283:0.535399:0.223283:0.521383:0.216914:0.521383:0.000000
⎠:@0.216914:0.567401:0.223283:0.567401:0.223283:0.553386:0.216914:0.553386:0.000000
⎟:@0.216914:0.546676:0.223283:0.546676:0.223283:0.532661:0.216914:0.532661:0.000000
⎟:@0.216914:0.558526:0.223283:0.558526:0.223283:0.544511:0.216914:0.544511:0.000000
=:@0.245424:0.549266:0.254529:0.549266:0.254529:0.535250:0.245424:0.535250:0.000000
⋅:@0.356244:0.541374:0.360390:0.541374:0.360390:0.527358:0.356244:0.527358:0.000000
+ ⎝ ⎝:@0.330040:0.561526:0.298900:0.562730:0.298900:0.548715:0.330040:0.547510:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.385831:0.561526:0.339145:0.561526:0.339145:0.547510:0.385831:0.547510:0.000000
⎛:@0.292541:0.540067:0.298910:0.540067:0.298910:0.526051:0.292541:0.526051:0.000000
−:@0.147130:0.542105:0.018689:0.542105:0.018689:0.533982:0.147130:0.533982:0.000000
−:@0.280848:0.542105:0.152407:0.542105:0.152407:0.533982:0.280848:0.533982:0.000000
Cos:@0.123432:0.548656:0.146270:0.548656:0.146270:0.534802:0.123432:0.534802:0.000000:0.000000:0.000000
AB:@0.179406:0.540764:0.203206:0.540764:0.203206:0.526911:0.179406:0.526911:0.000000:0.000000
A:@0.174182:0.560107:0.183088:0.560107:0.183088:0.546254:0.174182:0.546254:0.000000
B:@0.200519:0.560107:0.208480:0.560107:0.208480:0.546254:0.200519:0.546254:0.000000
Cos:@0.257156:0.548656:0.279994:0.548656:0.279994:0.534802:0.257156:0.534802:0.000000:0.000000:0.000000
1:@0.152349:0.541751:0.157039:0.541751:0.157039:0.533578:0.152349:0.533578:0.000000
1:@0.286067:0.541751:0.290757:0.541751:0.290757:0.533578:0.286067:0.533578:0.000000
2:@0.321130:0.554022:0.325821:0.554022:0.325821:0.545849:0.321130:0.545849:0.000000
2:@0.350388:0.554022:0.355078:0.554022:0.355078:0.545849:0.350388:0.545849:0.000000
2:@0.376907:0.554022:0.381597:0.554022:0.381597:0.545849:0.376907:0.545849:0.000000
2:@0.405646:0.554022:0.410336:0.554022:0.410336:0.545849:0.405646:0.545849:0.000000
3  4)(:@0.325418:0.540761:0.365802:0.540762:0.365802:0.526659:0.325418:0.526659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5  0),:@0.366134:0.540761:0.376549:0.540762:0.376549:0.526659:0.366134:0.526659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.313261:0.560914:0.321355:0.560914:0.321355:0.546811:0.313261:0.546811:0.000000
4:@0.342003:0.560914:0.350096:0.560914:0.350096:0.546811:0.342003:0.546811:0.000000
5:@0.369285:0.560914:0.377378:0.560914:0.377378:0.546811:0.369285:0.546811:0.000000
0:@0.397280:0.560914:0.405373:0.560914:0.405373:0.546811:0.397280:0.546811:0.000000
:@0.179920:0.530605:0.202923:0.530605:0.202923:0.516153:0.179920:0.516153:0.000000:0.000000
:@0.174695:0.549936:0.154776:0.549936:0.154776:0.535484:0.174695:0.535484:0.000000
:@0.201413:0.549936:0.181495:0.549936:0.181495:0.535484:0.201413:0.535484:0.000000
 :@0.189920:0.560105:0.193552:0.560105:0.193552:0.546002:0.189920:0.546002:0.000000
  ;:@0.230055:0.548653:0.227800:0.548653:0.227800:0.534551:0.230055:0.534551:0.000000:0.000000:0.000000
(,:@0.320708:0.540762:0.336082:0.540762:0.336082:0.526659:0.320708:0.526659:0.000000:0.000000
⎜:@0.292531:0.551341:0.298900:0.551341:0.298900:0.537325:0.292531:0.537325:0.000000
⎞:@0.416453:0.540064:0.422822:0.540064:0.422822:0.526048:0.416453:0.526048:0.000000
⎠:@0.416453:0.562718:0.422822:0.562718:0.422822:0.548702:0.416453:0.548702:0.000000
⎟:@0.416453:0.551329:0.422822:0.551329:0.422822:0.537313:0.416453:0.537313:0.000000
=:@0.444963:0.549250:0.454068:0.549250:0.454068:0.535234:0.444963:0.535234:0.000000
⎛:@0.492080:0.542491:0.498449:0.542491:0.498449:0.528475:0.492080:0.528475:0.000000
⎝:@0.492080:0.560278:0.498449:0.560278:0.498449:0.546263:0.492080:0.546263:0.000000
⎜:@0.492080:0.552461:0.498449:0.552461:0.498449:0.538446:0.492080:0.538446:0.000000
⎞:@0.522845:0.542490:0.529213:0.542490:0.529213:0.528475:0.522845:0.528475:0.000000
⎠:@0.522845:0.560277:0.529213:0.560277:0.529213:0.546262:0.522845:0.546262:0.000000
⎟:@0.522845:0.552461:0.529213:0.552461:0.529213:0.538445:0.522845:0.538445:0.000000
=:@0.111706:0.583902:0.073925:0.583902:0.073925:0.569887:0.111706:0.569887:0.000000
°:@0.158591:0.583902:0.120811:0.583902:0.120811:0.569887:0.158591:0.569887:0.000000
−:@0.480384:0.542105:0.485661:0.542105:0.485661:0.533982:0.480384:0.533982:0.000000
; :@0.424456:0.548656:0.433230:0.548656:0.433230:0.534553:0.424456:0.534553:0.000000:0.000000
,13:@0.139213:0.583310:0.158662:0.583313:0.158662:0.569211:0.139213:0.569207:0.000000:0.000000:0.000000
15:@0.502438:0.540764:0.518542:0.540764:0.518542:0.526662:0.502438:0.526662:0.000000:0.000000
,5:@0.509553:0.558415:0.520466:0.558415:0.520466:0.544312:0.509553:0.544312:0.000000:0.000000
Cos:@0.456681:0.548668:0.479518:0.548668:0.479518:0.534815:0.456681:0.534815:0.000000:0.000000:0.000000
1:@0.485601:0.541751:0.490291:0.541751:0.490291:0.533578:0.485601:0.533578:0.000000
5:@0.501539:0.558408:0.509633:0.558408:0.509633:0.544305:0.501539:0.544305:0.000000
53:@0.123436:0.583313:0.139540:0.583313:0.139540:0.569211:0.123436:0.569211:0.000000:0.000000
θ:@0.102124:0.548785:0.110284:0.548785:0.110284:0.534931:0.102124:0.534931:0.000000
θ:@0.102124:0.583450:0.110284:0.583450:0.110284:0.569597:0.102124:0.569597:0.000000
θ:@0.235816:0.548785:0.243976:0.548785:0.243976:0.534932:0.235816:0.534932:0.000000
θ:@0.434868:0.548785:0.443027:0.548785:0.443027:0.534932:0.434868:0.534932:0.000000
Paso único. :@0.102121:0.641635:0.189100:0.641635:0.189100:0.626057:0.102121:0.626057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinamos la proyección   sobre el vector  .:@0.189100:0.641635:0.518144:0.641635:0.518144:0.626736:0.189100:0.626736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.385820:0.641635:0.392856:0.641635:0.392856:0.626761:0.385820:0.626761:0.000000
1:@0.392856:0.644511:0.397622:0.644511:0.397622:0.635825:0.392856:0.635825:0.000000
v:@0.503429:0.641635:0.510465:0.641635:0.510465:0.626761:0.503429:0.626761:0.000000
2:@0.510463:0.644511:0.515229:0.644511:0.515229:0.635825:0.510463:0.635825:0.000000
V:@0.103582:0.676140:0.111791:0.676140:0.111791:0.661415:0.103582:0.661415:0.000000
VV:@0.154564:0.668224:0.180917:0.668224:0.180917:0.653498:0.154564:0.653498:0.000000:0.000000
V:@0.160319:0.687430:0.168528:0.687430:0.168528:0.672705:0.160319:0.672705:0.000000
VV:@0.196507:0.676152:0.227139:0.676152:0.227139:0.661427:0.196507:0.661427:0.000000:0.000000
v:@0.121439:0.677943:0.125476:0.677943:0.125476:0.669410:0.121439:0.669410:0.000000
v:@0.236779:0.677943:0.240816:0.677943:0.240816:0.669410:0.236779:0.669410:0.000000
2:@0.113712:0.676140:0.121805:0.676140:0.121805:0.661390:0.113712:0.661390:0.000000
2:@0.229060:0.676140:0.237153:0.676140:0.237153:0.661390:0.229060:0.661390:0.000000
15:@0.269659:0.668248:0.285763:0.668248:0.285763:0.653498:0.269659:0.653498:0.000000:0.000000
5:@0.270837:0.685899:0.278930:0.685899:0.278930:0.671149:0.270837:0.671149:0.000000
5 ( , 0);  2:@0.300325:0.676140:0.357104:0.676140:0.357104:0.661390:0.300325:0.661390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.126056:0.677943:0.130746:0.677943:0.130746:0.669395:0.126056:0.669395:0.000000
1:@0.161302:0.670023:0.165992:0.670023:0.165992:0.661474:0.161302:0.661474:0.000000
2:@0.180054:0.670023:0.184745:0.670023:0.184745:0.661474:0.180054:0.661474:0.000000
2:@0.167665:0.689226:0.172355:0.689226:0.172355:0.680677:0.167665:0.680677:0.000000
2:@0.179209:0.678831:0.183899:0.678831:0.183899:0.670282:0.179209:0.670282:0.000000
2:@0.203853:0.677943:0.208543:0.677943:0.208543:0.669395:0.203853:0.669395:0.000000
1:@0.241406:0.677943:0.246096:0.677943:0.246096:0.669395:0.241406:0.669395:0.000000
2:@0.278488:0.679004:0.283178:0.679004:0.283178:0.670456:0.278488:0.670456:0.000000
:@0.105372:0.665976:0.130266:0.665976:0.130266:0.651524:0.105372:0.651524:0.000000:0.000000
:@0.112106:0.665976:0.125639:0.665976:0.125639:0.651524:0.112106:0.651524:0.000000:0.000000
 :@0.156353:0.658055:0.185625:0.657096:0.185625:0.642645:0.156353:0.643603:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.198286:0.665021:0.240975:0.665980:0.240975:0.651528:0.198286:0.650570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= :@0.134152:0.676759:0.152261:0.676891:0.152261:0.662875:0.134152:0.662743:0.000000:0.000000:0.000000
⋅:@0.168035:0.668843:0.172181:0.668843:0.172181:0.654827:0.168035:0.654827:0.000000
:@0.145894:0.665619:0.152263:0.665619:0.152263:0.651603:0.145894:0.651603:0.000000
:@0.145892:0.692167:0.152261:0.692167:0.152261:0.678151:0.145892:0.678151:0.000000
:@0.145892:0.684347:0.152261:0.684347:0.152261:0.670331:0.145892:0.670331:0.000000
:@0.189527:0.665601:0.195896:0.665601:0.195896:0.651585:0.189527:0.651585:0.000000
:@0.189522:0.692167:0.195891:0.692167:0.195891:0.678151:0.189522:0.678151:0.000000
:@0.189522:0.676891:0.195891:0.676891:0.195891:0.662875:0.189522:0.662875:0.000000
:@0.189522:0.684347:0.195891:0.684347:0.195891:0.670331:0.189522:0.670331:0.000000
=:@0.249493:0.676741:0.258598:0.676741:0.258598:0.662726:0.249493:0.662726:0.000000
:@0.261219:0.669983:0.267587:0.669983:0.267587:0.655967:0.261219:0.655967:0.000000
:@0.261219:0.687770:0.267587:0.687770:0.267587:0.673754:0.261219:0.673754:0.000000
:@0.261219:0.679953:0.267587:0.679953:0.267587:0.665937:0.261219:0.665937:0.000000
:@0.288119:0.669983:0.294488:0.669983:0.294488:0.655967:0.288119:0.655967:0.000000
:@0.288119:0.687770:0.294488:0.687770:0.294488:0.673754:0.288119:0.673754:0.000000
:@0.288119:0.679953:0.294488:0.679953:0.294488:0.665937:0.288119:0.665937:0.000000
;:@0.210386:0.676119:0.213272:0.676119:0.213272:0.661369:0.210386:0.661369:0.000000
0:@0.316645:0.676119:0.324739:0.676119:0.324739:0.661369:0.316645:0.661369:0.000000
0):@0.402157:0.676140:0.414563:0.676140:0.414563:0.661390:0.402157:0.661390:0.000000:0.000000
V:@0.338886:0.676140:0.347095:0.676140:0.347095:0.661415:0.338886:0.661415:0.000000
v:@0.356736:0.677943:0.360773:0.677943:0.360773:0.669410:0.356736:0.669410:0.000000
3 (,:@0.385613:0.676140:0.396280:0.676145:0.396280:0.661395:0.385613:0.661390:0.000000:0.000000:0.000000:0.000000
1:@0.361355:0.677943:0.366046:0.677943:0.366046:0.669395:0.361355:0.669395:0.000000
:@0.340671:0.665976:0.365565:0.665976:0.365565:0.651524:0.340671:0.651524:0.000000:0.000000
:@0.347404:0.665976:0.360938:0.665976:0.360938:0.651524:0.347404:0.651524:0.000000:0.000000
=:@0.369462:0.676755:0.378567:0.676755:0.378567:0.662739:0.369462:0.662739:0.000000
Paso 1.:@0.102121:0.772036:0.154372:0.772036:0.154372:0.756458:0.102121:0.756458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Hallamos el módulo de cada vector :@0.154372:0.772036:0.397779:0.772036:0.397779:0.757137:0.154372:0.757137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y el de su suma.:@0.102121:0.787123:0.207611:0.787123:0.207611:0.772224:0.102121:0.772224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.105372:0.809459:0.135955:0.809459:0.135955:0.794734:0.105372:0.794734:0.000000:0.000000
AB:@0.110265:0.832474:0.140847:0.832474:0.140847:0.817749:0.110265:0.817749:0.000000:0.000000
A:@0.110265:0.859037:0.119171:0.859037:0.119171:0.844312:0.110265:0.844312:0.000000
:@0.105891:0.799295:0.135677:0.799295:0.135677:0.784843:0.105891:0.784843:0.000000:0.000000
:@0.110791:0.822316:0.140577:0.822316:0.140577:0.807865:0.110791:0.807865:0.000000:0.000000
:@0.110791:0.848878:0.117590:0.848878:0.117590:0.834427:0.110791:0.834427:0.000000
+=:@0.116546:0.810080:0.148604:0.810080:0.148604:0.796065:0.116546:0.796065:0.000000:0.000000
+−:@0.187313:0.810080:0.212821:0.810080:0.212821:0.796065:0.187313:0.796065:0.000000:0.000000
=−:@0.244979:0.810080:0.270768:0.810080:0.270768:0.796065:0.244979:0.796065:0.000000:0.000000
+:@0.121438:0.833095:0.130543:0.833095:0.130543:0.819080:0.121438:0.819080:0.000000
=:@0.149284:0.833095:0.158389:0.833095:0.158389:0.819080:0.149284:0.819080:0.000000
−:@0.177230:0.833095:0.186335:0.833095:0.186335:0.819080:0.177230:0.819080:0.000000
+:@0.205175:0.833095:0.214280:0.833095:0.214280:0.819080:0.205175:0.819080:0.000000
=:@0.235028:0.833095:0.244133:0.833095:0.244133:0.819080:0.235028:0.819080:0.000000
=:@0.126895:0.859658:0.136000:0.859658:0.136000:0.845642:0.126895:0.845642:0.000000
+:@0.166665:0.859658:0.175770:0.859658:0.175770:0.845642:0.166665:0.845642:0.000000
=:@0.196767:0.859658:0.205872:0.859658:0.205872:0.845642:0.196767:0.845642:0.000000
(, )( 32:@0.150926:0.809470:0.237930:0.809470:0.237930:0.794720:0.150926:0.794720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,) (, ):@0.220516:0.809470:0.297702:0.809470:0.297702:0.794720:0.220516:0.794720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.171989:0.832485:0.196402:0.832485:0.196402:0.817735:0.171989:0.817735:0.000000:0.000000
; :@0.235824:0.859048:0.244597:0.859037:0.244597:0.844287:0.235824:0.844298:0.000000:0.000000
23:@0.155636:0.809470:0.180829:0.809470:0.180829:0.794720:0.155636:0.794720:0.000000:0.000000
15:@0.270685:0.809470:0.293573:0.809470:0.293573:0.794720:0.270685:0.794720:0.000000:0.000000
1:@0.186252:0.832485:0.194345:0.832485:0.194345:0.817735:0.186252:0.817735:0.000000
5:@0.216602:0.832485:0.224696:0.832485:0.224696:0.817735:0.216602:0.817735:0.000000
26:@0.258015:0.832485:0.274118:0.832485:0.274118:0.817735:0.258015:0.817735:0.000000:0.000000
2:@0.149881:0.859048:0.157975:0.859048:0.157975:0.844298:0.149881:0.844298:0.000000
3:@0.178109:0.859048:0.186202:0.859048:0.186202:0.844298:0.178109:0.844298:0.000000
13:@0.218725:0.859048:0.234829:0.859048:0.234829:0.844298:0.218725:0.844298:0.000000:0.000000
2:@0.196259:0.825583:0.200949:0.825583:0.200949:0.817035:0.196259:0.817035:0.000000
2:@0.224248:0.825583:0.228938:0.825583:0.228938:0.817035:0.224248:0.817035:0.000000
2:@0.157764:0.852137:0.162454:0.852137:0.162454:0.843589:0.157764:0.843589:0.000000
2:@0.185984:0.852137:0.190674:0.852137:0.190674:0.843589:0.185984:0.843589:0.000000
 :@0.281299:0.809459:0.284931:0.809459:0.284931:0.794709:0.281299:0.794709:0.000000
B B:@0.251573:0.859036:0.259534:0.859036:0.259534:0.844311:0.251573:0.844311:0.000000:0.000000:0.000000
:@0.252469:0.848866:0.259269:0.848866:0.259269:0.834415:0.252469:0.834415:0.000000
=:@0.267976:0.859646:0.277081:0.859646:0.277081:0.845630:0.267976:0.845630:0.000000
−:@0.295921:0.859646:0.305026:0.859646:0.305026:0.845630:0.295921:0.845630:0.000000
+:@0.326172:0.859646:0.335277:0.859646:0.335277:0.845630:0.326172:0.845630:0.000000
=:@0.356274:0.859646:0.365379:0.859646:0.365379:0.845630:0.356274:0.845630:0.000000
( 3:@0.290697:0.859036:0.313070:0.859036:0.313070:0.844286:0.290697:0.844286:0.000000:0.000000:0.000000
):@0.313037:0.859036:0.317432:0.859036:0.317432:0.844286:0.313037:0.844286:0.000000
2:@0.337632:0.859036:0.345726:0.859036:0.345726:0.844286:0.337632:0.844286:0.000000
13:@0.378249:0.859036:0.394352:0.859036:0.394352:0.844286:0.378249:0.844286:0.000000:0.000000
2:@0.317253:0.852140:0.321943:0.852140:0.321943:0.843592:0.317253:0.843592:0.000000
2:@0.345473:0.852140:0.350163:0.852140:0.350163:0.843592:0.345473:0.843592:0.000000
Paso 2.:@0.410036:0.772036:0.462287:0.772036:0.462287:0.756458:0.410036:0.756458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Reemplazamos en la expresión del :@0.462287:0.772036:0.700584:0.772036:0.700584:0.757137:0.462287:0.757137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teorema de Pitágoras.:@0.410036:0.787123:0.554825:0.787123:0.554825:0.772224:0.410036:0.772224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.418188:0.814627:0.448770:0.814627:0.448770:0.799902:0.418188:0.799902:0.000000:0.000000
A:@0.481459:0.814627:0.490365:0.814627:0.490365:0.799902:0.481459:0.799902:0.000000
B:@0.520516:0.814627:0.528477:0.814627:0.528477:0.799902:0.520516:0.799902:0.000000
AB:@0.418188:0.889846:0.448770:0.889846:0.448770:0.875120:0.418188:0.875120:0.000000:0.000000
A:@0.481459:0.889846:0.490365:0.889846:0.490365:0.875120:0.481459:0.875120:0.000000
B:@0.520516:0.889846:0.528477:0.889846:0.528477:0.875120:0.520516:0.875120:0.000000
AB:@0.563022:0.889841:0.596291:0.889841:0.596291:0.875116:0.563022:0.875116:0.000000:0.000000
:@0.418701:0.804465:0.448487:0.804465:0.448487:0.790014:0.418701:0.790014:0.000000:0.000000
:@0.481972:0.804465:0.488772:0.804465:0.488772:0.790014:0.481972:0.790014:0.000000
:@0.521411:0.804465:0.528210:0.804465:0.528210:0.790014:0.521411:0.790014:0.000000
:@0.418705:0.879677:0.448492:0.879677:0.448492:0.865225:0.418705:0.865225:0.000000:0.000000
:@0.481977:0.879677:0.488776:0.879677:0.488776:0.865225:0.481977:0.865225:0.000000
:@0.521415:0.879677:0.528215:0.879677:0.528215:0.865225:0.521415:0.865225:0.000000
:@0.563541:0.878718:0.570341:0.878718:0.570341:0.864267:0.563541:0.864267:0.000000
+:@0.429353:0.815237:0.438458:0.815237:0.438458:0.801221:0.429353:0.801221:0.000000
=:@0.463849:0.815237:0.472954:0.815237:0.472954:0.801221:0.463849:0.801221:0.000000
+:@0.504167:0.815237:0.513272:0.815237:0.513272:0.801221:0.504167:0.801221:0.000000
(:@0.412297:0.848447:0.417820:0.848447:0.417820:0.823892:0.412297:0.823892:0.000000
) ( ) ( ):@0.448336:0.848447:0.575526:0.848447:0.575526:0.823892:0.448336:0.823892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.463372:0.843526:0.472477:0.843526:0.472477:0.829510:0.463372:0.829510:0.000000
+:@0.524058:0.843526:0.533163:0.843526:0.533163:0.829510:0.524058:0.829510:0.000000
=:@0.431521:0.865874:0.440626:0.865874:0.440626:0.851859:0.431521:0.851859:0.000000
+:@0.460362:0.865874:0.469467:0.865874:0.469467:0.851859:0.460362:0.851859:0.000000
+:@0.429348:0.890445:0.438453:0.890445:0.438453:0.876430:0.429348:0.876430:0.000000
=:@0.463845:0.890445:0.472950:0.890445:0.472950:0.876430:0.463845:0.876430:0.000000
+:@0.504163:0.890445:0.513268:0.890445:0.513268:0.876430:0.504163:0.876430:0.000000
⇒ ⊥:@0.543037:0.890445:0.585661:0.890445:0.585661:0.876430:0.543037:0.876430:0.000000:0.000000:0.000000
2:@0.454373:0.803488:0.459063:0.803488:0.459063:0.794939:0.454373:0.794939:0.000000
2:@0.495271:0.803488:0.499961:0.803488:0.499961:0.794939:0.495271:0.794939:0.000000
2:@0.534092:0.803488:0.538783:0.803488:0.538783:0.794939:0.534092:0.794939:0.000000
2:@0.453902:0.831599:0.458592:0.831599:0.458592:0.823051:0.453902:0.823051:0.000000
2:@0.515157:0.831599:0.519847:0.831599:0.519847:0.823051:0.515157:0.823051:0.000000
2:@0.575557:0.831599:0.580247:0.831599:0.580247:0.823051:0.575557:0.823051:0.000000
2:@0.454373:0.878698:0.459063:0.878698:0.459063:0.870150:0.454373:0.870150:0.000000
2:@0.495271:0.878698:0.499961:0.878698:0.499961:0.870150:0.495271:0.870150:0.000000
2:@0.534092:0.878698:0.538783:0.878698:0.538783:0.870150:0.534092:0.870150:0.000000
26:@0.429872:0.842916:0.445976:0.842916:0.445976:0.828166:0.429872:0.828166:0.000000:0.000000
13:@0.491634:0.842916:0.507738:0.842916:0.507738:0.828166:0.491634:0.828166:0.000000:0.000000
13:@0.552037:0.842916:0.568140:0.842916:0.568140:0.828166:0.552037:0.828166:0.000000:0.000000
26 13 13:@0.412292:0.865259:0.486875:0.865259:0.486875:0.850509:0.412292:0.850509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.589220:0.878714:0.596020:0.878714:0.596020:0.864263:0.589220:0.864263:0.000000:0.000000:0.000000
Ejemplos paso a paso:@0.096359:0.433273:0.251252:0.433273:0.251252:0.417909:0.096359:0.417909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.096359:0.460876:0.110585:0.460876:0.110585:0.443976:0.096359:0.443976:0.000000:0.000000
  Respondamos a las preguntas del problema inicial::@0.110585:0.460876:0.496436:0.460876:0.496436:0.444487:0.110585:0.444487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.124848:0.488163:0.139756:0.488163:0.139756:0.471263:0.124848:0.471263:0.000000:0.000000
  ¿Qué ángulo en grados forman las trayectorias de los dos aviones?:@0.139756:0.488163:0.639121:0.488163:0.639121:0.471775:0.139756:0.471775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.124848:0.612899:0.141065:0.612899:0.141065:0.595998:0.124848:0.595998:0.000000:0.000000
  ¿Cuál es la proyección ortogonal del vector   sobre el vector  ?:@0.141065:0.612899:0.625601:0.612907:0.625601:0.596518:0.141065:0.596510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.473459:0.612899:0.482580:0.612899:0.482580:0.596538:0.473459:0.596538:0.000000
1:@0.482585:0.616070:0.487828:0.616070:0.487828:0.606515:0.482585:0.606515:0.000000
V:@0.604216:0.612907:0.613338:0.612907:0.613338:0.596545:0.604216:0.596545:0.000000
2:@0.613336:0.616070:0.618579:0.616070:0.618579:0.606515:0.613336:0.606515:0.000000
cción y expresión:@0.117728:0.407174:0.242599:0.407174:0.242599:0.391810:0.117728:0.391810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.096132:0.407961:0.108221:0.407961:0.108221:0.390826:0.096132:0.390826:0.000000
Proyección ortogonal:@0.096359:0.098100:0.282650:0.098100:0.282650:0.079663:0.096359:0.079663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es la proyección de un vector sobre la dirección de otro vector.:@0.096359:0.121509:0.555054:0.121509:0.555054:0.105120:0.096359:0.105120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta proyección nos da un nuevo vector que tiene la misma dirección que el segun-:@0.096359:0.145228:0.712227:0.145228:0.712227:0.128839:0.096359:0.128839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do vector y cuya magnitud representa cuánto del primer vector ‘cae’ en esa dirección.:@0.096359:0.161825:0.712237:0.161825:0.712237:0.145436:0.096359:0.145436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.369188:0.209927:0.379560:0.209927:0.379560:0.193794:0.369188:0.193794:0.000000
λB:@0.357509:0.267443:0.374775:0.267443:0.374775:0.251310:0.357509:0.251310:0.000000:0.000000
B:@0.497877:0.266195:0.507147:0.266195:0.507147:0.250062:0.497877:0.250062:0.000000
C:@0.473454:0.211622:0.483844:0.211622:0.483844:0.195489:0.473454:0.195489:0.000000
En la figura se ha proyectado el vector   en la dirección del vector  , obteniéndose el :@0.096359:0.298227:0.716343:0.298227:0.716343:0.281838:0.096359:0.281838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.377550:0.298638:0.387445:0.298638:0.387445:0.282277:0.377550:0.282277:0.000000
:@0.378121:0.286287:0.385676:0.286287:0.385676:0.270230:0.378121:0.270230:0.000000
B:@0.577218:0.298398:0.586063:0.298398:0.586063:0.282037:0.577218:0.282037:0.000000
:@0.578213:0.286047:0.585769:0.286047:0.585769:0.269990:0.578213:0.269990:0.000000
vector   que resulta de::@0.096364:0.320355:0.276637:0.320360:0.276637:0.303971:0.096364:0.303966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λB:@0.147201:0.320569:0.164265:0.320569:0.164265:0.305176:0.147201:0.305176:0.000000:0.000000
:@0.155733:0.308219:0.163288:0.308219:0.163288:0.292162:0.155733:0.292162:0.000000
A:@0.341234:0.354803:0.351129:0.354803:0.351129:0.339410:0.341234:0.339410:0.000000
B λ:@0.382641:0.354803:0.382714:0.354803:0.382714:0.339410:0.382641:0.339410:0.000000:0.000000:0.000000
AB:@0.420067:0.346034:0.446511:0.346034:0.446511:0.330641:0.420067:0.330641:0.000000:0.000000
B:@0.424619:0.367333:0.433464:0.367333:0.433464:0.351940:0.424619:0.351940:0.000000
B:@0.459060:0.354803:0.467905:0.354803:0.467905:0.339410:0.459060:0.339410:0.000000
B:@0.349977:0.356807:0.355103:0.356807:0.355103:0.347886:0.349977:0.347886:0.000000
=:@0.360970:0.355480:0.336645:0.355480:0.336645:0.339908:0.360970:0.339908:0.000000
=:@0.395411:0.355480:0.371087:0.355480:0.371087:0.339908:0.395411:0.339908:0.000000
⋅:@0.431584:0.346712:0.436191:0.346712:0.436191:0.331139:0.431584:0.331139:0.000000
⎛:@0.408439:0.343102:0.415516:0.343102:0.415516:0.327529:0.408439:0.327529:0.000000
⎝:@0.408439:0.372616:0.415516:0.372616:0.415516:0.357043:0.408439:0.357043:0.000000
⎜:@0.408439:0.355646:0.415516:0.355646:0.415516:0.340074:0.408439:0.340074:0.000000
⎜:@0.408439:0.363931:0.415516:0.363931:0.415516:0.348358:0.408439:0.348358:0.000000
⎞:@0.450418:0.343102:0.457494:0.343102:0.457494:0.327529:0.450418:0.327529:0.000000
⎠:@0.450418:0.372616:0.457494:0.372616:0.457494:0.357043:0.450418:0.357043:0.000000
⎟:@0.450418:0.355646:0.457494:0.355646:0.457494:0.340074:0.450418:0.340074:0.000000
⎟:@0.450418:0.363931:0.457494:0.363931:0.457494:0.348358:0.450418:0.348358:0.000000
2:@0.439693:0.357789:0.444904:0.357789:0.444904:0.348707:0.439693:0.348707:0.000000
Los aviones son :@0.754864:0.131225:0.863235:0.131225:0.863235:0.116325:0.754864:0.116325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
responsables de una :@0.754864:0.146312:0.895886:0.146312:0.895886:0.131413:0.754864:0.131413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
parte significativa de las :@0.754864:0.161400:0.917645:0.161400:0.917645:0.146501:0.754864:0.146501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emisiones de gases de :@0.754864:0.176487:0.908718:0.176487:0.908718:0.161588:0.754864:0.161588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
efecto invernadero que :@0.754864:0.191575:0.914446:0.191575:0.914446:0.176676:0.754864:0.176676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
contribuyen al cambio :@0.754864:0.206663:0.909086:0.206663:0.909086:0.191764:0.754864:0.191764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
climático. Sin embargo, :@0.754864:0.221750:0.913775:0.221750:0.913775:0.206851:0.754864:0.206851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
muchas veces se utilizan :@0.754864:0.236838:0.922220:0.236838:0.922220:0.221939:0.754864:0.221939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para fines no esenciales o :@0.754864:0.251925:0.928636:0.251925:0.928636:0.237026:0.754864:0.237026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de manera poco :@0.754864:0.267013:0.868629:0.267013:0.868629:0.252114:0.754864:0.252114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consciente.:@0.754864:0.282101:0.830499:0.282101:0.830499:0.267202:0.754864:0.267202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debate con tus :@0.754864:0.394642:0.853500:0.394642:0.853500:0.379768:0.754864:0.379768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
compañeros de clase sobre :@0.754864:0.409729:0.928449:0.409729:0.928449:0.394855:0.754864:0.394855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la responsabilidad que :@0.754864:0.424817:0.901062:0.424817:0.901062:0.409943:0.754864:0.409943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tienen las aerolíneas y los :@0.754864:0.439904:0.917260:0.439904:0.917260:0.425031:0.754864:0.425031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
viajeros en reducir ese :@0.754864:0.454992:0.894661:0.454992:0.894661:0.440118:0.754864:0.440118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
impacto:@0.754864:0.470080:0.808656:0.470080:0.808656:0.455206:0.754864:0.455206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.808656:0.470080:0.811571:0.470080:0.811571:0.455181:0.808656:0.455181:0.000000
Desarrollo :@0.801065:0.091870:0.882923:0.091870:0.882923:0.074969:0.801065:0.074969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sostenible:@0.799600:0.105700:0.877415:0.105700:0.877415:0.088799:0.799600:0.088799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.945603:0.350684:0.945603:0.307858:0.933692:0.307858:0.933692:0.350684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vectores ortogonales :@0.755397:0.581484:0.925951:0.581484:0.925951:0.566585:0.755397:0.566585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se utilizan en acústica, :@0.755397:0.596572:0.906403:0.596572:0.906403:0.581673:0.755397:0.581673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para analizar la :@0.755397:0.611659:0.857502:0.611659:0.857502:0.596760:0.755397:0.596760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propagación del sonido y :@0.755397:0.626747:0.929253:0.626747:0.929253:0.611848:0.755397:0.611848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las vibraciones en :@0.755397:0.641835:0.877019:0.641835:0.877019:0.626936:0.755397:0.626936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferentes direcciones. Por :@0.755397:0.656922:0.933356:0.656922:0.933356:0.642023:0.755397:0.642023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo, al estudiar cómo :@0.755397:0.672010:0.931731:0.672010:0.931731:0.657111:0.755397:0.657111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una onda sonora :@0.755397:0.687097:0.872094:0.687097:0.872094:0.672198:0.755397:0.672198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interactúa con superficies :@0.755397:0.702185:0.930558:0.702185:0.930558:0.687286:0.755397:0.687286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o materiales, se :@0.755397:0.717273:0.861036:0.717273:0.861036:0.702374:0.755397:0.702374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
descomponen sus :@0.755397:0.732360:0.881961:0.732360:0.881961:0.717461:0.755397:0.717461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
componentes de presión :@0.755397:0.747448:0.927207:0.747448:0.927207:0.732549:0.755397:0.732549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y movimiento en :@0.755397:0.762535:0.872812:0.762535:0.872812:0.747636:0.755397:0.747636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
direcciones :@0.755397:0.777623:0.835272:0.777623:0.835272:0.762724:0.755397:0.762724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
perpendiculares, lo que :@0.755397:0.792711:0.915749:0.792711:0.915749:0.777812:0.755397:0.777812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
permite evaluar :@0.755397:0.807798:0.863950:0.807798:0.863950:0.792899:0.755397:0.792899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fenómenos como la :@0.755397:0.822886:0.892716:0.822886:0.892716:0.807987:0.755397:0.807987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reflexión, absorción o :@0.755397:0.837974:0.901392:0.837974:0.901392:0.823074:0.755397:0.823074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
difracción del sonido.:@0.755397:0.853061:0.897690:0.853061:0.897690:0.838162:0.755397:0.838162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Averigua la velocidad del :@0.755397:0.871707:0.916134:0.871707:0.916134:0.856833:0.755397:0.856833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sonido en diferentes :@0.755397:0.886795:0.884606:0.886795:0.884606:0.871921:0.755397:0.871921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
materiales. Haz un cuadro :@0.755397:0.901882:0.924576:0.901882:0.924576:0.887008:0.755397:0.887008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comparativo.:@0.755397:0.916970:0.839979:0.916970:0.839979:0.902096:0.755397:0.902096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
    Comunicacional:@0.762002:0.549043:0.898062:0.549043:0.898062:0.532143:0.762002:0.532143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000