78:@0.058599:0.966558:0.074760:0.966558:0.074760:0.950778:0.058599:0.950778:0.000000:0.000000
M.5.2.3. Sumar, restar vectores de forma geométrica y de forma analítica, aplicando propiedades de los números reales y de los vectores en el plano.:@0.143128:0.952010:0.776770:0.952010:0.776770:0.941968:0.143128:0.941968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Operaciones con vectores en el plano:@0.404235:0.120539:0.856599:0.120539:0.856599:0.075879:0.404235:0.075879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto de todos los vectores del plano se denota con  . Se  :@0.404235:0.157929:0.895917:0.157929:0.895917:0.141431:0.404235:0.141431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.850591:0.158045:0.861341:0.158045:0.861341:0.141576:0.850591:0.141576:0.000000
2:@0.861282:0.160600:0.865804:0.160600:0.865804:0.151818:0.861282:0.151818:0.000000
definen las operaciones de adición y el producto de escalares por :@0.404248:0.175280:0.895988:0.175280:0.895988:0.158782:0.404248:0.158782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891774:0.175280:0.895917:0.175280:0.895917:0.158782:0.891774:0.158782:0.000000
vectores de :@0.404248:0.192630:0.490073:0.192630:0.490073:0.176133:0.404248:0.176133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V .:@0.490073:0.192746:0.510388:0.192746:0.510388:0.176277:0.490073:0.176277:0.000000:0.000000:0.000000
2 :@0.500809:0.195302:0.507536:0.195302:0.507536:0.186520:0.500809:0.186520:0.000000:0.000000
Adición de vectores en V:@0.404235:0.228729:0.603048:0.228729:0.603048:0.211047:0.404235:0.211047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.603049:0.231004:0.608043:0.231004:0.608043:0.221983:0.603049:0.221983:0.000000
Definición:@0.404235:0.253027:0.484318:0.253027:0.484318:0.236082:0.404235:0.236082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  , :@0.404235:0.270537:0.463243:0.270544:0.463243:0.254046:0.404235:0.254040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v V:@0.443417:0.270660:0.502044:0.270660:0.502044:0.254191:0.443417:0.254191:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.477558:0.270038:0.491294:0.270038:0.491294:0.252326:0.477558:0.252326:0.000000
2:@0.502042:0.273215:0.506564:0.273215:0.506564:0.264434:0.502042:0.264434:0.000000
. Existen :@0.506565:0.270544:0.566748:0.270544:0.566748:0.254046:0.506565:0.254046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.565977:0.270660:0.593045:0.270660:0.593045:0.254191:0.565977:0.254191:0.000000:0.000000:0.000000:0.000000
 puntos del plano, tal que (:@0.593045:0.270544:0.779357:0.270544:0.779357:0.254046:0.593045:0.254046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.779357:0.270660:0.806425:0.270660:0.806425:0.254191:0.779357:0.254191:0.000000:0.000000:0.000000:0.000000
)   :@0.806425:0.270544:0.833708:0.270544:0.833708:0.254046:0.806425:0.254046:0.000000:0.000000:0.000000:0.000000
∈:@0.815830:0.270038:0.829566:0.270038:0.829566:0.252326:0.815830:0.252326:0.000000
AB u:@0.836662:0.271917:0.885291:0.270660:0.885291:0.254191:0.836662:0.255448:0.000000:0.000000:0.000000:0.000000
=  . :@0.859751:0.270544:0.895911:0.270544:0.895911:0.254046:0.859751:0.254046:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891769:0.270544:0.895911:0.270544:0.895911:0.254046:0.891769:0.254046:0.000000
A partir de   construimos un punto   del plano, tal que :@0.404242:0.289775:0.829189:0.289775:0.829189:0.273277:0.404242:0.273277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.492436:0.289890:0.501626:0.289890:0.501626:0.273421:0.492436:0.273421:0.000000
C:@0.679521:0.289890:0.689558:0.289890:0.689558:0.273421:0.679521:0.273421:0.000000
BC:@0.834091:0.289897:0.852913:0.289897:0.852913:0.273428:0.834091:0.273428:0.000000:0.000000
=  . :@0.856655:0.289781:0.895911:0.289781:0.895911:0.273283:0.856655:0.273283:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.876346:0.289897:0.884129:0.289897:0.884129:0.273428:0.876346:0.273428:0.000000
 :@0.891769:0.289781:0.895911:0.289781:0.895911:0.273283:0.891769:0.273283:0.000000
El vector :@0.404242:0.307753:0.470474:0.307753:0.470474:0.291256:0.404242:0.291256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AC:@0.474392:0.309133:0.495622:0.309133:0.495622:0.292664:0.474392:0.292664:0.000000:0.000000
 se llama suma de los vectores   y  , lo cual se denota  :@0.500829:0.307760:0.895919:0.307760:0.895919:0.291263:0.500829:0.291263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.721620:0.307876:0.730829:0.307876:0.730829:0.291407:0.721620:0.291407:0.000000
v:@0.753485:0.307876:0.761268:0.307876:0.761268:0.291407:0.753485:0.291407:0.000000
u:@0.406380:0.325855:0.415589:0.325855:0.415589:0.309387:0.406380:0.309387:0.000000
 +  , esto es, :@0.419312:0.325740:0.515743:0.325740:0.515743:0.309242:0.419312:0.309242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.440812:0.325855:0.448595:0.325855:0.448595:0.309387:0.440812:0.309387:0.000000
AC:@0.519461:0.327113:0.540691:0.327113:0.540691:0.310644:0.519461:0.310644:0.000000:0.000000
 =   +  .:@0.545898:0.325740:0.616991:0.325740:0.616991:0.309242:0.545898:0.309242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.567135:0.325855:0.576344:0.325855:0.576344:0.309387:0.567135:0.309387:0.000000
v:@0.601566:0.325855:0.609349:0.325855:0.609349:0.309387:0.601566:0.309387:0.000000
Debemos enfatizar que esta suma es independiente de la selección de :@0.404245:0.343090:0.895846:0.343090:0.895846:0.326593:0.404245:0.326593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sus representantes. Además, el bipunto (:@0.404245:0.360441:0.689349:0.360441:0.689349:0.343943:0.404245:0.343943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, C:@0.689349:0.360557:0.717650:0.360557:0.717650:0.344088:0.689349:0.344088:0.000000:0.000000:0.000000:0.000000
) es un representante del :@0.717650:0.360441:0.895931:0.360441:0.895931:0.343943:0.717650:0.343943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector :@0.404245:0.378414:0.454045:0.378414:0.454045:0.361916:0.404245:0.361916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AC:@0.457750:0.379794:0.478980:0.379794:0.478980:0.363325:0.457750:0.363325:0.000000:0.000000
 =   +  .:@0.484189:0.378421:0.552378:0.378421:0.552378:0.361923:0.484189:0.361923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.505426:0.378536:0.514634:0.378536:0.514634:0.362067:0.505426:0.362067:0.000000
v:@0.539857:0.378536:0.547640:0.378536:0.547640:0.362067:0.539857:0.362067:0.000000
En la figura 2.14. se muestran los vectores  ,  , así como el vector  :@0.404229:0.395771:0.895910:0.395771:0.895910:0.379274:0.404229:0.379274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.716938:0.395887:0.746682:0.395887:0.746682:0.379418:0.716938:0.379418:0.000000:0.000000:0.000000
u:@0.406380:0.413238:0.415589:0.413238:0.415589:0.396769:0.406380:0.396769:0.000000
 +  .:@0.419312:0.413122:0.453606:0.413122:0.453606:0.396624:0.419312:0.396624:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.440812:0.413238:0.448595:0.413238:0.448595:0.396769:0.440812:0.396769:0.000000
Dados los vectores  ,   :@0.404229:0.430473:0.590762:0.430473:0.590762:0.413975:0.404229:0.413975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.549798:0.430588:0.581733:0.430588:0.581733:0.414120:0.549798:0.414120:0.000000:0.000000:0.000000
∈:@0.592669:0.429967:0.606405:0.429967:0.606405:0.412255:0.592669:0.412255:0.000000
V:@0.606405:0.430588:0.617155:0.430588:0.617155:0.414120:0.606405:0.414120:0.000000
2 :@0.617162:0.433144:0.623890:0.433144:0.623890:0.424362:0.617162:0.424362:0.000000:0.000000
, existen :@0.624909:0.430473:0.687105:0.430473:0.687105:0.413975:0.624909:0.413975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B, C, D:@0.689024:0.430588:0.758463:0.430588:0.758463:0.414120:0.689024:0.414120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 puntos del plano, :@0.758463:0.430473:0.895909:0.430473:0.895909:0.413975:0.758463:0.413975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tales que::@0.404225:0.447824:0.470594:0.447824:0.470594:0.431326:0.404225:0.431326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{:@0.584708:0.472341:0.593955:0.472341:0.593955:0.445966:0.584708:0.445966:0.000000
{:@0.584612:0.499770:0.593859:0.499770:0.593859:0.473395:0.584612:0.473395:0.000000
}:@0.759928:0.472008:0.769175:0.472008:0.769175:0.446447:0.759928:0.446447:0.000000
}:@0.763588:0.499430:0.772836:0.499430:0.772836:0.473869:0.763588:0.473869:0.000000
(:@0.593399:0.470731:0.599815:0.470731:0.599815:0.447612:0.593399:0.447612:0.000000
) (:@0.637478:0.470731:0.659556:0.470731:0.659556:0.447612:0.637478:0.447612:0.000000:0.000000:0.000000
):@0.697220:0.470731:0.703635:0.470731:0.703635:0.447612:0.697220:0.447612:0.000000
(:@0.593303:0.498161:0.599718:0.498161:0.599718:0.475042:0.593303:0.475042:0.000000
) (:@0.638634:0.498161:0.660712:0.498161:0.660712:0.475042:0.638634:0.475042:0.000000:0.000000:0.000000
):@0.699628:0.498161:0.706043:0.498161:0.706043:0.475042:0.699628:0.475042:0.000000
(:@0.719722:0.470153:0.726138:0.470153:0.726138:0.448173:0.719722:0.448173:0.000000
):@0.754072:0.470153:0.760488:0.470153:0.760488:0.448173:0.754072:0.448173:0.000000
(:@0.722131:0.497578:0.728546:0.497578:0.728546:0.475599:0.722131:0.475599:0.000000
):@0.757733:0.497578:0.764148:0.497578:0.764148:0.475599:0.757733:0.475599:0.000000
==:@0.543928:0.467854:0.581630:0.467854:0.581630:0.451573:0.543928:0.451573:0.000000:0.000000
==:@0.543986:0.495282:0.581533:0.495282:0.581533:0.479002:0.543986:0.479002:0.000000:0.000000
AB u:@0.520212:0.467333:0.566796:0.467333:0.566796:0.450864:0.520212:0.450864:0.000000:0.000000:0.000000:0.000000
A B:@0.601666:0.467333:0.631854:0.467333:0.631854:0.450864:0.601666:0.450864:0.000000:0.000000:0.000000
A B:@0.661407:0.467333:0.691596:0.467333:0.691596:0.450864:0.661407:0.450864:0.000000:0.000000:0.000000
A B:@0.728007:0.467333:0.753322:0.467333:0.753322:0.450864:0.728007:0.450864:0.000000:0.000000:0.000000
CD v:@0.519076:0.494762:0.565697:0.494762:0.565697:0.478293:0.519076:0.478293:0.000000:0.000000:0.000000:0.000000
C D:@0.600433:0.494762:0.633049:0.494762:0.633049:0.478293:0.600433:0.478293:0.000000:0.000000:0.000000
C D:@0.661407:0.494762:0.694043:0.494762:0.694043:0.478293:0.661407:0.478293:0.000000:0.000000:0.000000
C D:@0.729259:0.494762:0.757021:0.494762:0.757021:0.478293:0.729259:0.478293:0.000000:0.000000:0.000000
,:@0.618850:0.467217:0.621605:0.467217:0.621605:0.450720:0.618850:0.450720:0.000000
|:@0.645918:0.467217:0.650927:0.467217:0.650927:0.450720:0.645918:0.450720:0.000000
,:@0.678575:0.467217:0.681330:0.467217:0.681330:0.450720:0.678575:0.450720:0.000000
,:@0.740301:0.467217:0.743056:0.467217:0.743056:0.450720:0.740301:0.450720:0.000000
.:@0.770189:0.467217:0.772944:0.467217:0.772944:0.450720:0.770189:0.450720:0.000000
,:@0.617589:0.494646:0.620344:0.494646:0.620344:0.478148:0.617589:0.478148:0.000000
|:@0.647065:0.494646:0.652074:0.494646:0.652074:0.478148:0.647065:0.478148:0.000000
,:@0.678575:0.494642:0.681330:0.494642:0.681330:0.478144:0.678575:0.478144:0.000000
,:@0.741553:0.494642:0.744308:0.494642:0.744308:0.478144:0.741553:0.478144:0.000000
.:@0.773854:0.494642:0.776609:0.494642:0.776609:0.478144:0.773854:0.478144:0.000000
1:@0.611931:0.469436:0.616848:0.469436:0.616848:0.459888:0.611931:0.459888:0.000000
1:@0.630932:0.469436:0.635849:0.469436:0.635849:0.459888:0.630932:0.459888:0.000000
1:@0.671665:0.469436:0.676583:0.469436:0.676583:0.459888:0.671665:0.459888:0.000000
1:@0.690666:0.469436:0.695583:0.469436:0.695583:0.459888:0.690666:0.459888:0.000000
1:@0.610682:0.496861:0.615599:0.496861:0.615599:0.487312:0.610682:0.487312:0.000000
1:@0.632091:0.496861:0.637009:0.496861:0.637009:0.487312:0.632091:0.487312:0.000000
1:@0.671665:0.496861:0.676583:0.496861:0.676583:0.487312:0.671665:0.487312:0.000000
1:@0.693075:0.496861:0.697992:0.496861:0.697992:0.487312:0.693075:0.487312:0.000000
En la figura 2.15. se muestran el vector   y tres bipuntos equipolentes :@0.404235:0.528000:0.895898:0.528000:0.895898:0.511503:0.404235:0.511503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.675116:0.528116:0.684325:0.528116:0.684325:0.511647:0.675116:0.511647:0.000000
con el bipunto (:@0.404231:0.545973:0.518915:0.545973:0.518915:0.529475:0.404231:0.529475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A, B:@0.518915:0.546089:0.546754:0.546089:0.546754:0.529620:0.518915:0.529620:0.000000:0.000000:0.000000:0.000000
) con :@0.546754:0.545973:0.587943:0.545973:0.587943:0.529475:0.546754:0.529475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.591662:0.547353:0.612045:0.547353:0.612045:0.530884:0.591662:0.530884:0.000000:0.000000
=  .:@0.614748:0.545980:0.647530:0.545980:0.647530:0.529482:0.614748:0.529482:0.000000:0.000000:0.000000:0.000000
u:@0.631844:0.546095:0.641053:0.546095:0.641053:0.529627:0.631844:0.529627:0.000000
Saberes previos:@0.199646:0.101454:0.307805:0.101454:0.307805:0.085981:0.199646:0.085981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿A qué es igual la longi-:@0.199884:0.130082:0.350787:0.130082:0.350787:0.115019:0.199884:0.115019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tud o norma de un vector   :@0.153341:0.145924:0.343992:0.145924:0.343992:0.130861:0.153341:0.130861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.328572:0.146356:0.336860:0.146356:0.336860:0.131534:0.328572:0.131534:0.000000
del plano?:@0.153351:0.161766:0.218980:0.161766:0.218980:0.146703:0.153351:0.146703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199644:0.205353:0.363492:0.205353:0.363492:0.189881:0.199644:0.189881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si un bote, en reposo, :@0.199880:0.233981:0.343132:0.233981:0.343132:0.218917:0.199880:0.218917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recibe el empuje de la corriente :@0.153337:0.249823:0.360898:0.249823:0.360898:0.234759:0.153337:0.234759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del agua y del viento, ¿cuál será :@0.153337:0.265665:0.357132:0.265665:0.357132:0.250601:0.153337:0.250601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su dirección en ese momento?:@0.153337:0.281507:0.350871:0.281507:0.350871:0.266443:0.153337:0.266443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dirección de :@0.201805:0.295688:0.267674:0.295688:0.267674:0.284212:0.201805:0.284212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la corriente:@0.201805:0.307758:0.257288:0.307758:0.257288:0.296282:0.201805:0.296282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dirección del viento:@0.204633:0.358040:0.304141:0.358040:0.304141:0.346564:0.204633:0.346564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bote:@0.204633:0.335419:0.227778:0.335419:0.227778:0.323942:0.204633:0.323942:0.000000:0.000000:0.000000:0.000000
p:@0.302154:0.741269:0.313634:0.741269:0.313634:0.731245:0.302154:0.731245:0.000000
 Figura 2.14.:@0.313634:0.741977:0.370994:0.741977:0.370994:0.730501:0.313634:0.730501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.193724:0.559264:0.202012:0.559264:0.202012:0.544442:0.193724:0.544442:0.000000
v:@0.298668:0.570847:0.305672:0.570847:0.305672:0.556026:0.298668:0.556026:0.000000
C:@0.205052:0.621408:0.213343:0.621408:0.213343:0.607803:0.205052:0.607803:0.000000
B:@0.334964:0.667011:0.342556:0.667011:0.342556:0.653407:0.334964:0.653407:0.000000
=:@0.200166:0.675456:0.209158:0.675456:0.209158:0.661851:0.200166:0.661851:0.000000
+:@0.227364:0.675456:0.236356:0.675456:0.236356:0.661851:0.227364:0.661851:0.000000
A:@0.199736:0.719590:0.209046:0.719590:0.209046:0.705986:0.199736:0.705986:0.000000
u:@0.239188:0.697023:0.247476:0.697023:0.247476:0.682201:0.239188:0.682201:0.000000
u v:@0.215108:0.675030:0.246151:0.675030:0.246151:0.660208:0.215108:0.660208:0.000000:0.000000:0.000000
v:@0.290301:0.643562:0.297306:0.643562:0.297306:0.628740:0.290301:0.628740:0.000000
AB:@0.276546:0.703716:0.292852:0.703716:0.292852:0.690541:0.276546:0.690541:0.000000:0.000000
BC:@0.248389:0.656116:0.263446:0.656116:0.263446:0.642941:0.248389:0.642941:0.000000:0.000000
AC:@0.179484:0.675718:0.196469:0.675718:0.196469:0.662543:0.179484:0.662543:0.000000:0.000000
En la figura 2.16. se muestran el vector   y dos puntos equipolentes  :@0.404235:0.694242:0.895919:0.694242:0.895919:0.677744:0.404235:0.677744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.684433:0.694358:0.692217:0.694358:0.692217:0.677889:0.684433:0.677889:0.000000
(:@0.404250:0.713472:0.410203:0.713472:0.410203:0.696975:0.404250:0.696975:0.000000
C, D:@0.410203:0.713588:0.439198:0.713588:0.439198:0.697119:0.410203:0.697119:0.000000:0.000000:0.000000:0.000000
) del vector :@0.439198:0.713472:0.524714:0.713472:0.524714:0.696975:0.439198:0.696975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
CD:@0.527262:0.713594:0.548897:0.713594:0.548897:0.697126:0.527262:0.697126:0.000000:0.000000
 =  .:@0.551501:0.713479:0.585144:0.713479:0.585144:0.696981:0.551501:0.696981:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.573000:0.713594:0.580783:0.713594:0.580783:0.697126:0.573000:0.697126:0.000000
En la suma   +  , se elige un representante de  ; por ejemplo  :@0.404224:0.880566:0.895913:0.880570:0.895913:0.864073:0.404224:0.864069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.497232:0.880686:0.506441:0.880686:0.506441:0.864217:0.497232:0.864217:0.000000
v:@0.538713:0.880686:0.546496:0.880686:0.546496:0.864217:0.538713:0.864217:0.000000
u:@0.780262:0.880686:0.789471:0.880686:0.789471:0.864217:0.780262:0.864217:0.000000
(:@0.404245:0.897921:0.410198:0.897921:0.410198:0.881423:0.404245:0.881423:0.000000
A , B:@0.410198:0.898037:0.443733:0.898037:0.443733:0.881568:0.410198:0.881568:0.000000:0.000000:0.000000:0.000000:0.000000
1 :@0.421456:0.900593:0.428183:0.900593:0.428183:0.891812:0.421456:0.891812:0.000000:0.000000
1:@0.443732:0.900593:0.448254:0.900593:0.448254:0.891812:0.443732:0.891812:0.000000
), y a partir del punto   se construye el punto  , de modo que :@0.448255:0.897921:0.895918:0.897921:0.895918:0.881423:0.448255:0.881423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.599795:0.898037:0.608985:0.898037:0.608985:0.881568:0.599795:0.881568:0.000000
1:@0.608984:0.900593:0.613506:0.900593:0.613506:0.891812:0.608984:0.891812:0.000000
C:@0.772368:0.898037:0.782406:0.898037:0.782406:0.881568:0.772368:0.881568:0.000000
1 :@0.782396:0.900593:0.789124:0.900593:0.789124:0.891812:0.782396:0.891812:0.000000:0.000000
(:@0.404234:0.915893:0.410187:0.915893:0.410187:0.899396:0.404234:0.899396:0.000000
B , C:@0.410187:0.916009:0.443827:0.916016:0.443827:0.899548:0.410187:0.899540:0.000000:0.000000:0.000000:0.000000:0.000000
1 :@0.419375:0.918573:0.426103:0.918573:0.426103:0.909791:0.419375:0.909791:0.000000:0.000000
1:@0.443829:0.918573:0.448351:0.918573:0.448351:0.909791:0.443829:0.909791:0.000000
) :@0.448350:0.915901:0.458445:0.915901:0.458445:0.899403:0.448350:0.899403:0.000000:0.000000
∈:@0.458908:0.915395:0.472644:0.915395:0.472644:0.897682:0.458908:0.897682:0.000000
CD:@0.475198:0.917274:0.496833:0.917274:0.496833:0.900805:0.475198:0.900805:0.000000:0.000000
 =  . El bipunto (:@0.499437:0.915901:0.623780:0.915901:0.623780:0.899403:0.499437:0.899403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.521843:0.916016:0.529626:0.916016:0.529626:0.899548:0.521843:0.899548:0.000000
A , C:@0.623780:0.916016:0.659501:0.916016:0.659501:0.899548:0.623780:0.899548:0.000000:0.000000:0.000000:0.000000:0.000000
1 :@0.635051:0.918573:0.641778:0.918573:0.641778:0.909791:0.635051:0.909791:0.000000:0.000000
1:@0.659503:0.918573:0.664025:0.918573:0.664025:0.909791:0.659503:0.909791:0.000000
) es un representante del vector :@0.664024:0.915901:0.895910:0.915901:0.895910:0.899403:0.664024:0.899403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AC:@0.407950:0.935253:0.429180:0.935253:0.429180:0.918784:0.407950:0.918784:0.000000:0.000000
 =   +  .:@0.434389:0.933880:0.502185:0.933880:0.502185:0.917383:0.434389:0.917383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.455626:0.933996:0.464835:0.933996:0.464835:0.917527:0.455626:0.917527:0.000000
v:@0.490057:0.933996:0.497840:0.933996:0.497840:0.917527:0.490057:0.917527:0.000000
B:@0.790262:0.592223:0.797853:0.592223:0.797853:0.578619:0.790262:0.578619:0.000000
2:@0.797854:0.595440:0.802376:0.595440:0.802376:0.586658:0.797854:0.586658:0.000000
A:@0.684140:0.642832:0.693450:0.642832:0.693450:0.629228:0.684140:0.629228:0.000000
2:@0.693450:0.646049:0.697972:0.646049:0.697972:0.637267:0.693450:0.637267:0.000000
B:@0.713877:0.594133:0.721469:0.594133:0.721469:0.580529:0.713877:0.580529:0.000000
1:@0.721468:0.597350:0.725990:0.597350:0.725990:0.588568:0.721468:0.588568:0.000000
A:@0.607754:0.644742:0.617064:0.644742:0.617064:0.631137:0.607754:0.631137:0.000000
1:@0.617065:0.647959:0.621588:0.647959:0.621588:0.639177:0.617065:0.639177:0.000000
B:@0.618483:0.594629:0.626074:0.594629:0.626074:0.581024:0.618483:0.581024:0.000000
A:@0.510771:0.645237:0.520082:0.645237:0.520082:0.631632:0.510771:0.631632:0.000000
AB:@0.535835:0.606002:0.552141:0.606002:0.552141:0.592827:0.535835:0.592827:0.000000:0.000000
B:@0.860484:0.592401:0.868076:0.592401:0.868076:0.578796:0.860484:0.578796:0.000000
3:@0.868075:0.595619:0.872597:0.595619:0.872597:0.586837:0.868075:0.586837:0.000000
A:@0.754361:0.643010:0.763671:0.643010:0.763671:0.629405:0.754361:0.629405:0.000000
3:@0.763672:0.646228:0.768195:0.646228:0.768195:0.637446:0.763672:0.637446:0.000000
u:@0.448486:0.618510:0.457695:0.618510:0.457695:0.602041:0.448486:0.602041:0.000000
p:@0.822929:0.662623:0.834409:0.662623:0.834409:0.652598:0.822929:0.652598:0.000000
 Figura 2.15.:@0.834409:0.663331:0.891769:0.663331:0.891769:0.651854:0.834409:0.651854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.822929:0.847655:0.834409:0.847655:0.834409:0.837630:0.822929:0.837630:0.000000
 :@0.834409:0.848363:0.837291:0.848363:0.837291:0.836886:0.834409:0.836886:0.000000
Figura 2.16.:@0.837291:0.848363:0.891769:0.848363:0.891769:0.836886:0.837291:0.836886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.519372:0.772484:0.528985:0.772484:0.528985:0.758879:0.519372:0.758879:0.000000
C:@0.623550:0.828742:0.631842:0.828742:0.631842:0.815137:0.623550:0.815137:0.000000
C:@0.737866:0.814803:0.746158:0.814803:0.746158:0.801198:0.737866:0.801198:0.000000
1:@0.746166:0.818025:0.750688:0.818025:0.750688:0.809243:0.746166:0.809243:0.000000
D:@0.627043:0.754169:0.636656:0.754169:0.636656:0.740564:0.627043:0.740564:0.000000
1:@0.636656:0.757387:0.641178:0.757387:0.641178:0.748605:0.636656:0.748605:0.000000
C:@0.824775:0.814757:0.833067:0.814757:0.833067:0.801152:0.824775:0.801152:0.000000
2:@0.833067:0.817975:0.837590:0.817975:0.837590:0.809193:0.833067:0.809193:0.000000
D:@0.713944:0.754118:0.723557:0.754118:0.723557:0.740514:0.713944:0.740514:0.000000
2:@0.723557:0.757337:0.728079:0.757337:0.728079:0.748555:0.723557:0.748555:0.000000
v:@0.484123:0.803737:0.491128:0.803737:0.491128:0.788915:0.484123:0.788915:0.000000
CD:@0.551892:0.798902:0.571363:0.798902:0.571363:0.784080:0.551892:0.784080:0.000000:0.000000
Competencia :@0.199644:0.825478:0.297267:0.825478:0.297267:0.810005:0.199644:0.810005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.838046:0.311603:0.838046:0.311603:0.822573:0.199644:0.822573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.193071:0.862520:0.329536:0.862520:0.329536:0.847457:0.193071:0.847457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.153335:0.878362:0.308107:0.878362:0.308107:0.863299:0.153335:0.863299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A la suma de dos vectores    :@0.153335:0.897769:0.347822:0.897768:0.347822:0.882705:0.153335:0.882706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.328623:0.898201:0.336910:0.898201:0.336910:0.883379:0.328623:0.883379:0.000000
y   la denotamos con   +  .:@0.153347:0.913610:0.348222:0.913610:0.348222:0.898547:0.153347:0.898546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.166434:0.914042:0.173439:0.914042:0.173439:0.899220:0.166434:0.899220:0.000000
u:@0.304744:0.914043:0.313032:0.914043:0.313032:0.899221:0.304744:0.899221:0.000000
v:@0.335980:0.914042:0.342985:0.914042:0.342985:0.899220:0.335980:0.899220:0.000000