150:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
 Vectores geométricos en el plano:@0.073089:0.043661:0.371606:0.043661:0.371606:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.4. Multiplicación de un número real por un vector de V  :@0.293660:0.136836:0.742570:0.136836:0.742570:0.119889:0.293660:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.733008:0.140009:0.738760:0.140009:0.738760:0.130129:0.733008:0.130129:0.000000
Sean :@0.293653:0.171340:0.332430:0.171340:0.332430:0.154906:0.293653:0.154906:0.000000:0.000000:0.000000:0.000000:0.000000
u V:@0.332530:0.171340:0.365755:0.171340:0.365755:0.154934:0.332530:0.154934:0.000000:0.000000:0.000000
[:@0.341586:0.171202:0.356919:0.171202:0.356919:0.157153:0.341586:0.157153:0.000000
2:@0.365522:0.174519:0.370759:0.174519:0.370759:0.164938:0.365522:0.164938:0.000000
, :@0.370604:0.171347:0.377580:0.171347:0.377580:0.154913:0.370604:0.154913:0.000000:0.000000
a:@0.377691:0.170792:0.388938:0.170792:0.388938:0.157076:0.377691:0.157076:0.000000
[:@0.388662:0.171208:0.403995:0.171208:0.403995:0.157159:0.388662:0.157159:0.000000
ℝ:@0.403719:0.173129:0.418113:0.173129:0.418113:0.157861:0.403719:0.157861:0.000000
. A continuación se define la multiplicación del escalar   por el vector  .:@0.417800:0.171347:0.926890:0.171347:0.926890:0.154913:0.417800:0.154913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.805402:0.170792:0.816649:0.170792:0.816649:0.157076:0.805402:0.157076:0.000000
u:@0.914631:0.171347:0.923945:0.171347:0.923945:0.154941:0.914631:0.154941:0.000000
Esto es, :@0.293643:0.187988:0.349668:0.187988:0.349668:0.171555:0.293643:0.171555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.349859:0.187434:0.361106:0.187434:0.361106:0.173718:0.349859:0.173718:0.000000
u:@0.360848:0.187988:0.370162:0.187988:0.370162:0.171582:0.360848:0.171582:0.000000
. Debemos tener presente que dado  , existen  ,   puntos del plano, tales que :@0.370107:0.187988:0.930805:0.187988:0.930805:0.171555:0.370107:0.171555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.633184:0.187988:0.642498:0.187988:0.642498:0.171582:0.633184:0.171582:0.000000
A B:@0.703904:0.187988:0.729527:0.187988:0.729527:0.171582:0.703904:0.171582:0.000000:0.000000:0.000000
( ,  ) :@0.293662:0.204630:0.331838:0.204630:0.331838:0.188196:0.293662:0.188196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.298282:0.204630:0.323445:0.204630:0.323445:0.188224:0.298282:0.188224:0.000000:0.000000:0.000000
[:@0.331562:0.204492:0.346896:0.204492:0.346896:0.190443:0.331562:0.190443:0.000000
AB:@0.346619:0.204630:0.365082:0.204630:0.365082:0.188224:0.346619:0.188224:0.000000:0.000000
   :@0.364843:0.204630:0.387704:0.204630:0.387704:0.188196:0.364843:0.188196:0.000000:0.000000:0.000000
5:@0.368616:0.204076:0.383949:0.204076:0.383949:0.190360:0.368616:0.190360:0.000000
u.:@0.387447:0.204630:0.399835:0.204630:0.399835:0.188224:0.387447:0.188224:0.000000:0.000000
Definición:@0.293662:0.239134:0.371631:0.239134:0.371631:0.222465:0.293662:0.222465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.293662:0.273638:0.333631:0.273638:0.333631:0.257205:0.293662:0.257205:0.000000:0.000000:0.000000:0.000000:0.000000
u V:@0.334323:0.273638:0.368174:0.273638:0.368174:0.257232:0.334323:0.257232:0.000000:0.000000:0.000000
[:@0.343674:0.273500:0.359008:0.273500:0.359008:0.259451:0.343674:0.259451:0.000000
2:@0.368203:0.276825:0.373440:0.276825:0.373440:0.267244:0.368203:0.267244:0.000000
 y :@0.373466:0.273652:0.390327:0.273652:0.390327:0.257218:0.373466:0.257218:0.000000:0.000000:0.000000
a:@0.391008:0.273098:0.402255:0.273098:0.402255:0.259382:0.391008:0.259382:0.000000
[:@0.402310:0.273514:0.417643:0.273514:0.417643:0.259465:0.402310:0.259465:0.000000
ℝ:@0.417698:0.275435:0.432093:0.275435:0.432093:0.260167:0.417698:0.260167:0.000000
. Fijado el punto  , se construye  , tal que     :@0.432148:0.273652:0.779327:0.273652:0.779327:0.257218:0.432148:0.257218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.556673:0.273652:0.566558:0.273652:0.566558:0.257246:0.556673:0.257246:0.000000
B:@0.672749:0.273652:0.681585:0.273652:0.681585:0.257246:0.672749:0.257246:0.000000
u:@0.745863:0.273652:0.755177:0.273652:0.755177:0.257246:0.745863:0.257246:0.000000
5:@0.759907:0.273098:0.775241:0.273098:0.775241:0.259382:0.759907:0.259382:0.000000
AB:@0.779990:0.273652:0.798747:0.273652:0.798747:0.257246:0.779990:0.257246:0.000000:0.000000
 y a partir de   se:@0.798784:0.273652:0.926924:0.273652:0.926924:0.257218:0.798784:0.257218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.897520:0.273652:0.906356:0.273652:0.906356:0.257246:0.897520:0.257246:0.000000
construye un punto  , tal que     :@0.293670:0.290294:0.550470:0.290294:0.550470:0.273860:0.293670:0.273860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.445107:0.290294:0.455010:0.290294:0.455010:0.273888:0.445107:0.273888:0.000000
v:@0.518754:0.290294:0.526485:0.290294:0.526485:0.273888:0.518754:0.273888:0.000000
5 a:@0.531087:0.289739:0.562269:0.289739:0.562269:0.276024:0.531087:0.276024:0.000000:0.000000:0.000000
AB:@0.562287:0.290294:0.581026:0.290294:0.581026:0.273888:0.562287:0.273888:0.000000:0.000000
   :@0.581044:0.290294:0.605010:0.290294:0.605010:0.273860:0.581044:0.273860:0.000000:0.000000:0.000000
5:@0.585628:0.289739:0.600961:0.289739:0.600961:0.276024:0.585628:0.276024:0.000000
AC:@0.605563:0.290294:0.625056:0.290294:0.625056:0.273888:0.605563:0.273888:0.000000:0.000000
. El bipunto ( ,  ) es representante de un :@0.625074:0.290294:0.930889:0.290294:0.930889:0.273860:0.625074:0.273860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A C:@0.718749:0.290294:0.746360:0.290294:0.746360:0.273888:0.718749:0.273888:0.000000:0.000000:0.000000
vector :@0.293670:0.306936:0.343570:0.306936:0.343570:0.290502:0.293670:0.290502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AC:@0.343462:0.306936:0.362863:0.306936:0.362863:0.290530:0.343462:0.290530:0.000000:0.000000
 denominado producto de   por  , al que se lo denota :@0.362808:0.306936:0.762595:0.306936:0.762595:0.290502:0.362808:0.290502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.560244:0.306381:0.571491:0.306381:0.571491:0.292666:0.560244:0.292666:0.000000
u:@0.604440:0.306936:0.613754:0.306936:0.613754:0.290530:0.604440:0.290530:0.000000
a:@0.762374:0.306381:0.773621:0.306381:0.773621:0.292666:0.762374:0.292666:0.000000
u:@0.773529:0.306936:0.782843:0.306936:0.782843:0.290530:0.773529:0.290530:0.000000
, es decir, :@0.782769:0.306936:0.851844:0.306936:0.851844:0.290502:0.782769:0.290502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AC:@0.851686:0.306936:0.871087:0.306936:0.871087:0.290530:0.851686:0.290530:0.000000:0.000000
   :@0.871032:0.306936:0.894262:0.306936:0.894262:0.290502:0.871032:0.290502:0.000000:0.000000:0.000000
5 a:@0.874990:0.306381:0.905435:0.306381:0.905435:0.292666:0.874990:0.292666:0.000000:0.000000:0.000000
u:@0.905343:0.306936:0.914657:0.306936:0.914657:0.290530:0.905343:0.290530:0.000000
.:@0.914584:0.306936:0.917787:0.306936:0.917787:0.290502:0.914584:0.290502:0.000000
La norma del vector resultante :@0.293670:0.341440:0.519115:0.341440:0.519115:0.325006:0.293670:0.325006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.518865:0.340885:0.530111:0.340885:0.530111:0.327170:0.518865:0.327170:0.000000
u :@0.530019:0.341440:0.542573:0.341440:0.542573:0.325034:0.530019:0.325034:0.000000:0.000000
es ІІ:@0.542518:0.341440:0.569816:0.341440:0.569816:0.325006:0.542518:0.325006:0.000000:0.000000:0.000000:0.000000:0.000000
a 5 a:@0.569705:0.340885:0.628001:0.340885:0.628001:0.327170:0.569705:0.327170:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.580860:0.341440:0.590174:0.341440:0.590174:0.325034:0.580860:0.325034:0.000000
ІІ І І ІІ ІІ.:@0.590101:0.341440:0.662625:0.341440:0.662625:0.325006:0.590101:0.325006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  u:@0.631719:0.341440:0.651875:0.341440:0.651875:0.325034:0.631719:0.325034:0.000000:0.000000:0.000000
En la Figura 2.8. se muestran los vectores :@0.293652:0.375944:0.591483:0.375944:0.591483:0.359510:0.293652:0.359510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u AB :@0.591150:0.375944:0.637518:0.375944:0.637518:0.359538:0.591150:0.359538:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.600390:0.375389:0.615723:0.375389:0.615723:0.361674:0.600390:0.361674:0.000000
y :@0.637462:0.375944:0.649519:0.375944:0.649519:0.359510:0.637462:0.359510:0.000000:0.000000
a 5:@0.649427:0.375389:0.688395:0.375389:0.688395:0.361674:0.649427:0.361674:0.000000:0.000000:0.000000
u   AC:@0.660582:0.375944:0.710944:0.375944:0.710944:0.359538:0.660582:0.359538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.710889:0.375944:0.714092:0.375944:0.714092:0.359510:0.710889:0.359510:0.000000
Figura 2.9:@0.569319:0.515264:0.639222:0.515264:0.639222:0.498830:0.569319:0.498830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.414954:0.441658:0.424268:0.441658:0.424268:0.425252:0.414954:0.425252:0.000000
u:@0.531169:0.445590:0.540483:0.445590:0.540483:0.429184:0.531169:0.429184:0.000000
u:@0.780674:0.438442:0.789988:0.438442:0.789988:0.422036:0.780674:0.422036:0.000000
a:@0.599403:0.416802:0.610650:0.416802:0.610650:0.403087:0.599403:0.403087:0.000000
u:@0.610558:0.417357:0.619872:0.417357:0.619872:0.400951:0.610558:0.400951:0.000000
a.:@0.465709:0.478628:0.492197:0.478628:0.492197:0.464912:0.465709:0.464912:0.000000:0.000000
0:@0.492105:0.479183:0.501088:0.479183:0.501088:0.462749:0.492105:0.462749:0.000000
a,:@0.662096:0.478628:0.688584:0.478628:0.688584:0.464912:0.662096:0.464912:0.000000:0.000000
0:@0.688492:0.479183:0.697475:0.479183:0.697475:0.462749:0.688492:0.462749:0.000000
a:@0.531184:0.478628:0.542431:0.478628:0.542431:0.464912:0.531184:0.464912:0.000000
u:@0.542339:0.479183:0.551653:0.479183:0.551653:0.462777:0.542339:0.462777:0.000000
Obsérvese que si     0, los vectores   y :@0.293660:0.556937:0.581473:0.556937:0.581473:0.540503:0.293660:0.540503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a .:@0.419388:0.556382:0.449392:0.556382:0.449392:0.542666:0.419388:0.542666:0.000000:0.000000:0.000000
u:@0.556706:0.556937:0.566021:0.556937:0.566021:0.540531:0.556706:0.540531:0.000000
a:@0.580976:0.556382:0.592223:0.556382:0.592223:0.542666:0.580976:0.542666:0.000000
u :@0.592104:0.556937:0.604639:0.556937:0.604639:0.540531:0.592104:0.540531:0.000000:0.000000
tienen la misma dirección y sentido. Además, :@0.604234:0.556937:0.930698:0.556937:0.930698:0.540503:0.604234:0.540503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si 0       1, :@0.293667:0.573578:0.389587:0.573578:0.389587:0.557145:0.293667:0.557145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, a ,:@0.320615:0.573024:0.369854:0.573024:0.369854:0.559308:0.320615:0.559308:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.389293:0.573024:0.400539:0.573024:0.400539:0.559308:0.389293:0.559308:0.000000
u :@0.400447:0.573578:0.413001:0.573578:0.413001:0.557172:0.400447:0.557172:0.000000:0.000000
es un vector más pequeño que  , mientras que si     1, el vector :@0.412780:0.573578:0.887408:0.573578:0.887408:0.557145:0.412780:0.557145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.641601:0.573578:0.650915:0.573578:0.650915:0.557172:0.641601:0.557172:0.000000
a .:@0.771372:0.573024:0.801615:0.573024:0.801615:0.559308:0.771372:0.559308:0.000000:0.000000:0.000000
a:@0.887061:0.573024:0.898308:0.573024:0.898308:0.559308:0.887061:0.559308:0.000000
u:@0.898216:0.573578:0.907530:0.573578:0.907530:0.557172:0.898216:0.557172:0.000000
 es :@0.907457:0.573578:0.930963:0.573578:0.930963:0.557145:0.907457:0.557145:0.000000:0.000000:0.000000:0.000000
más grande que  (véase Figura 2.8.). :@0.293667:0.590220:0.563134:0.590220:0.563134:0.573786:0.293667:0.573786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u :@0.415983:0.590220:0.428537:0.590220:0.428537:0.573814:0.415983:0.573814:0.000000:0.000000
Si   < 0, los vectores   y :@0.293667:0.624724:0.475291:0.624724:0.475291:0.608291:0.293667:0.608291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.310473:0.624170:0.321719:0.624170:0.321719:0.610454:0.310473:0.610454:0.000000
u:@0.449411:0.624724:0.458725:0.624724:0.458725:0.608318:0.449411:0.608318:0.000000
a:@0.475678:0.624170:0.486925:0.624170:0.486925:0.610454:0.475678:0.610454:0.000000
u :@0.486925:0.624724:0.499552:0.624724:0.499552:0.608318:0.486925:0.608318:0.000000:0.000000
tienen la misma dirección, pero son de sentidos opuestos. :@0.499865:0.624724:0.931266:0.624724:0.931266:0.608291:0.499865:0.608291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.926932:0.624724:0.930963:0.624724:0.930963:0.608291:0.926932:0.608291:0.000000
En la gráfica se muestra el caso :@0.293685:0.641366:0.521099:0.641366:0.521099:0.624932:0.293685:0.624932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a,:@0.520794:0.640811:0.547282:0.640811:0.547282:0.627096:0.520794:0.627096:0.000000:0.000000
0.:@0.547190:0.641366:0.559302:0.641366:0.559302:0.624932:0.547190:0.624932:0.000000:0.000000
Definición:@0.293685:0.675870:0.371655:0.675870:0.371655:0.659201:0.293685:0.659201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.293685:0.710374:0.333357:0.710374:0.333357:0.693941:0.293685:0.693941:0.000000:0.000000:0.000000:0.000000:0.000000
u, v  V:@0.333739:0.710374:0.385501:0.710374:0.385501:0.693968:0.333739:0.693968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.361093:0.710236:0.376426:0.710236:0.376426:0.696187:0.361093:0.696187:0.000000
2:@0.385435:0.713566:0.390672:0.713566:0.390672:0.703985:0.385435:0.703985:0.000000
 con :@0.390653:0.710393:0.426842:0.710393:0.426842:0.693959:0.390653:0.693959:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.427228:0.710393:0.436542:0.710393:0.436542:0.693987:0.427228:0.693987:0.000000
Þ:@0.436524:0.709839:0.451857:0.709839:0.451857:0.696123:0.436524:0.696123:0.000000
0. Se dice que   y   son colineales si y solo si existe :@0.451820:0.710393:0.827185:0.710393:0.827185:0.693959:0.451820:0.693959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.558472:0.710393:0.592360:0.710393:0.592360:0.693987:0.558472:0.693987:0.000000:0.000000:0.000000
a:@0.827660:0.709839:0.838906:0.709839:0.838906:0.696123:0.827660:0.696123:0.000000
[:@0.838870:0.710255:0.854203:0.710255:0.854203:0.696206:0.838870:0.696206:0.000000
ℝ:@0.854166:0.712176:0.868560:0.712176:0.868560:0.696908:0.854166:0.696908:0.000000
, tal que:@0.868505:0.710393:0.926911:0.710393:0.926911:0.693959:0.868505:0.693959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.293684:0.727035:0.301415:0.727035:0.301415:0.710629:0.293684:0.710629:0.000000
5a:@0.301341:0.726480:0.327829:0.726480:0.327829:0.712765:0.301341:0.712765:0.000000:0.000000
u:@0.327737:0.727035:0.337051:0.727035:0.337051:0.710629:0.327737:0.710629:0.000000
.:@0.336977:0.727035:0.340180:0.727035:0.340180:0.710601:0.336977:0.710601:0.000000
Nótese que los vectores   y :@0.293665:0.761539:0.498547:0.761539:0.498547:0.745105:0.293665:0.745105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.472860:0.761539:0.482174:0.761539:0.482174:0.745133:0.472860:0.745133:0.000000
a:@0.498878:0.760984:0.510125:0.760984:0.510125:0.747269:0.498878:0.747269:0.000000
u:@0.510061:0.761539:0.519375:0.761539:0.519375:0.745133:0.510061:0.745133:0.000000
 son paralelos; son del mismo sentido si     0, y son de :@0.519320:0.761539:0.930906:0.761539:0.930906:0.745105:0.519320:0.745105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a .:@0.813320:0.760984:0.844189:0.760984:0.844189:0.747269:0.813320:0.747269:0.000000:0.000000:0.000000
sentidos opuestos si     0.:@0.293647:0.778181:0.490807:0.778181:0.490807:0.761747:0.293647:0.761747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a ,:@0.444384:0.777626:0.474829:0.777626:0.474829:0.763911:0.444384:0.763911:0.000000:0.000000:0.000000
Aprende la siguiente :@0.082305:0.567527:0.219561:0.567527:0.219561:0.552587:0.082305:0.552587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.082305:0.582656:0.237567:0.582656:0.237567:0.567716:0.082305:0.567716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• Denotamos los vectores:@0.082305:0.597785:0.245531:0.597785:0.245531:0.582845:0.082305:0.582845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con letras latinas, como:@0.082305:0.612914:0.233171:0.612914:0.233171:0.597974:0.082305:0.597974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v a b:@0.082305:0.628043:0.132206:0.628043:0.132206:0.613128:0.082305:0.613128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,  ,  ,  .:@0.090538:0.628043:0.134883:0.628043:0.134883:0.613103:0.090538:0.613103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mientras que   las:@0.082272:0.643172:0.198890:0.643172:0.198890:0.628232:0.082272:0.628232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.170359:0.643172:0.178776:0.643172:0.178776:0.628257:0.170359:0.628257:0.000000
magnitudes escalares:@0.082272:0.658301:0.221404:0.658301:0.221404:0.643361:0.082272:0.643361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con letras griegas, como:@0.082272:0.673429:0.239085:0.673429:0.239085:0.658490:0.082272:0.658490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.082272:0.688054:0.108561:0.688054:0.108561:0.675585:0.082272:0.675585:0.000000:0.000000:0.000000
,  .:@0.092245:0.688558:0.111221:0.688558:0.111221:0.673619:0.092245:0.673619:0.000000:0.000000:0.000000:0.000000
• Al producto de   por :@0.082272:0.703687:0.229463:0.703687:0.229463:0.688748:0.082272:0.688748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.190021:0.703183:0.200245:0.703183:0.200245:0.690714:0.190021:0.690714:0.000000
u:@0.229195:0.703687:0.237662:0.703687:0.237662:0.688773:0.229195:0.688773:0.000000
lo denotamos con :@0.082305:0.718816:0.204044:0.718816:0.204044:0.703876:0.082305:0.703876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.203693:0.718312:0.213917:0.718312:0.213917:0.705843:0.203693:0.705843:0.000000
u:@0.213666:0.718816:0.222133:0.718816:0.222133:0.703902:0.213666:0.703902:0.000000
.:@0.221899:0.718816:0.224811:0.718816:0.224811:0.703876:0.221899:0.703876:0.000000
Simbología :@0.087319:0.535721:0.181137:0.535721:0.181137:0.518774:0.087319:0.518774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.087319:0.552363:0.180984:0.552363:0.180984:0.535416:0.087319:0.535416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La suma de vectores :@0.078581:0.184893:0.217044:0.184893:0.217044:0.169953:0.078581:0.169953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se puede realizar por el :@0.078581:0.200022:0.234701:0.200022:0.234701:0.185082:0.078581:0.185082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
método del paralelogramo, :@0.078581:0.215151:0.262717:0.215151:0.262717:0.200211:0.078581:0.200211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es decir, trazar sobre cada :@0.078581:0.230280:0.250777:0.230280:0.250777:0.215340:0.078581:0.215340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector una recta paralela :@0.078581:0.245409:0.244633:0.245409:0.244633:0.230469:0.078581:0.230469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al otro vector, formando :@0.078581:0.260538:0.241172:0.260538:0.241172:0.245598:0.078581:0.245598:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un paralelogramo cuya :@0.078581:0.275667:0.234986:0.275667:0.234986:0.260727:0.078581:0.260727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diagonal es la suma.:@0.078581:0.290796:0.211465:0.290796:0.211465:0.275856:0.078581:0.275856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.139772:0.376224:0.149031:0.376224:0.149031:0.359818:0.139772:0.359818:0.000000
a b:@0.168231:0.339414:0.201925:0.339414:0.201925:0.323008:0.168231:0.323008:0.000000:0.000000:0.000000
1:@0.177425:0.338859:0.192758:0.338859:0.192758:0.325144:0.177425:0.325144:0.000000
a:@0.088068:0.327621:0.097327:0.327621:0.097327:0.311215:0.088068:0.311215:0.000000
Practica en tu cuaderno.:@0.078581:0.391038:0.237810:0.391038:0.237810:0.376098:0.078581:0.376098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dados los vectores  ,   :@0.078581:0.406167:0.232700:0.406167:0.232700:0.391227:0.078581:0.391227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q:@0.205842:0.406167:0.229035:0.406167:0.229035:0.391252:0.205842:0.391252:0.000000:0.000000:0.000000
encuentra el vector suma :@0.078581:0.421296:0.250118:0.421296:0.250118:0.406356:0.078581:0.406356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.078581:0.436425:0.086998:0.436425:0.086998:0.421510:0.078581:0.421510:0.000000
    .:@0.086931:0.436425:0.119244:0.436425:0.119244:0.421485:0.086931:0.421485:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.090529:0.435920:0.104468:0.435920:0.104468:0.423451:0.090529:0.423451:0.000000
q:@0.107982:0.436425:0.116399:0.436425:0.116399:0.421510:0.107982:0.421510:0.000000
Competencia :@0.078581:0.145303:0.187141:0.145303:0.187141:0.128356:0.078581:0.128356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.161945:0.176057:0.161945:0.176057:0.144998:0.078581:0.144998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000