148:@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 El conjunto de todos los vectores del plano se denota con . Se definen las operaciones :@0.293660:0.240389:0.931098:0.240389:0.931098:0.223955:0.293660:0.223955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V:@0.713695:0.240389:0.722807:0.240389:0.722807:0.223983:0.713695:0.223983:0.000000 2:@0.722737:0.243561:0.727973:0.243561:0.727973:0.233980:0.722737:0.233980:0.000000 de adición y el producto de escalares por vectores de .:@0.293662:0.257031:0.704396:0.257031:0.704396:0.240597:0.293662:0.240597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V:@0.682994:0.257031:0.692105:0.257031:0.692105:0.240625:0.682994:0.240625:0.000000 2:@0.692045:0.260203:0.697282:0.260203:0.697282:0.250622:0.692045:0.250622:0.000000 2.1 Adición de vectores en V:@0.293657:0.285405:0.513607:0.285405:0.513607:0.268458:0.293657:0.268458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.513481:0.288575:0.519233:0.288575:0.519233:0.278695:0.513481:0.278695:0.000000 Definición:@0.293660:0.312051:0.371630:0.312051:0.371630:0.295381:0.293660:0.295381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , :@0.293660:0.339413:0.366682:0.339413:0.366682:0.322979:0.293660:0.322979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.336070:0.339413:0.362466:0.339413:0.362466:0.323007:0.336070:0.323007:0.000000:0.000000:0.000000 [:@0.368394:0.339274:0.383727:0.339274:0.383727:0.325226:0.368394:0.325226:0.000000 V:@0.383985:0.339413:0.393096:0.339413:0.393096:0.323007:0.383985:0.323007:0.000000 2:@0.393265:0.342586:0.398502:0.342586:0.398502:0.333005:0.393265:0.333005:0.000000 . Existen , puntos del plano, tal que ( , ) :@0.398630:0.339414:0.764253:0.339414:0.764253:0.322980:0.398630:0.322980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.466643:0.339414:0.494716:0.339414:0.494716:0.323008:0.466643:0.323008:0.000000:0.000000:0.000000 A B:@0.705549:0.339414:0.733605:0.339414:0.733605:0.323008:0.705549:0.323008:0.000000:0.000000:0.000000 [:@0.744631:0.339275:0.759964:0.339275:0.759964:0.325227:0.744631:0.325227:0.000000 AB :@0.765965:0.339414:0.788367:0.339414:0.788367:0.323008:0.765965:0.323008:0.000000:0.000000:0.000000 5:@0.789766:0.338859:0.805099:0.338859:0.805099:0.325144:0.789766:0.325144:0.000000 . A partir de :@0.805357:0.339414:0.930948:0.339414:0.930948:0.322980:0.805357:0.322980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.811100:0.339414:0.820414:0.339414:0.820414:0.323008:0.811100:0.323008:0.000000 B:@0.918081:0.339414:0.926916:0.339414:0.926916:0.323008:0.918081:0.323008:0.000000 construimos un punto del plano, tal que :@0.293672:0.356056:0.616412:0.356056:0.616412:0.339622:0.293672:0.339622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.466498:0.356056:0.476401:0.356056:0.476401:0.339650:0.466498:0.339650:0.000000 BC :@0.617455:0.356056:0.639655:0.356056:0.639655:0.339650:0.617455:0.339650:0.000000:0.000000:0.000000 5:@0.640483:0.355501:0.655816:0.355501:0.655816:0.341785:0.640483:0.341785:0.000000 . El vector :@0.655927:0.356056:0.745647:0.356056:0.745647:0.339622:0.655927:0.339622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.660952:0.356056:0.668683:0.356056:0.668683:0.339650:0.660952:0.339650:0.000000 AC :@0.746641:0.356056:0.769584:0.356056:0.769584:0.339650:0.746641:0.339650:0.000000:0.000000:0.000000 se llama suma de los :@0.770420:0.356056:0.930894:0.356056:0.930894:0.339622:0.770420:0.339622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vectores y , lo cual se denota , esto es, :@0.293672:0.372698:0.630401:0.372698:0.630401:0.356264:0.293672:0.356264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.358907:0.372698:0.391801:0.372698:0.391801:0.356292:0.358907:0.356292:0.000000:0.000000:0.000000 u:@0.525843:0.372698:0.535157:0.372698:0.535157:0.356292:0.525843:0.356292:0.000000 1:@0.539041:0.372143:0.554374:0.372143:0.554374:0.358427:0.539041:0.358427:0.000000 v:@0.558239:0.372698:0.565970:0.372698:0.565970:0.356292:0.558239:0.356292:0.000000 AC:@0.630267:0.372698:0.649668:0.372698:0.649668:0.356292:0.630267:0.356292:0.000000:0.000000 .:@0.649613:0.372698:0.716026:0.372698:0.716026:0.356264:0.649613:0.356264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 1:@0.653570:0.372143:0.701300:0.372143:0.701300:0.358427:0.653570:0.358427:0.000000:0.000000:0.000000 u:@0.672769:0.372698:0.682083:0.372698:0.682083:0.356292:0.672769:0.356292:0.000000 v:@0.705166:0.372698:0.712897:0.372698:0.712897:0.356292:0.705166:0.356292:0.000000 Debemos enfatizar que esta suma es independiente de la selección de sus representantes. :@0.293672:0.400060:0.930931:0.400060:0.930931:0.383626:0.293672:0.383626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Además, el bipunto (:@0.293672:0.416701:0.444055:0.416701:0.444055:0.400268:0.293672:0.400268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A, C:@0.443857:0.416701:0.470069:0.416701:0.470069:0.400295:0.443857:0.400295:0.000000:0.000000:0.000000:0.000000 ) es un representante del vector :@0.470032:0.416701:0.703855:0.416701:0.703855:0.400268:0.470032:0.400268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AC :@0.703583:0.416701:0.726231:0.416701:0.726231:0.400295:0.703583:0.400295:0.000000:0.000000:0.000000 5 1:@0.726169:0.416147:0.773899:0.416147:0.773899:0.402431:0.726169:0.402431:0.000000:0.000000:0.000000 .:@0.741410:0.416701:0.788624:0.416701:0.788624:0.400268:0.741410:0.400268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.745367:0.416701:0.754682:0.416701:0.754682:0.400295:0.745367:0.400295:0.000000 v:@0.777764:0.416701:0.785495:0.416701:0.785495:0.400295:0.777764:0.400295:0.000000 En la Figura 2.1. se muestran los vectores , , así como el vector .:@0.293672:0.444063:0.801160:0.444063:0.801160:0.427630:0.293672:0.427630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.591170:0.444063:0.615210:0.444063:0.615210:0.427657:0.591170:0.427657:0.000000:0.000000:0.000000 u:@0.757903:0.444063:0.767217:0.444063:0.767217:0.427657:0.757903:0.427657:0.000000 1:@0.771101:0.443509:0.786434:0.443509:0.786434:0.429793:0.771101:0.429793:0.000000 v:@0.790300:0.444063:0.798031:0.444063:0.798031:0.427657:0.790300:0.427657:0.000000 Dados los vectores , :@0.293653:0.471425:0.461638:0.471425:0.461638:0.454992:0.293653:0.454992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.433641:0.471425:0.457680:0.471425:0.457680:0.455019:0.433641:0.455019:0.000000:0.000000:0.000000 [:@0.461564:0.471287:0.476898:0.471287:0.476898:0.457238:0.461564:0.457238:0.000000 V:@0.476806:0.471425:0.485917:0.471425:0.485917:0.455019:0.476806:0.455019:0.000000 2:@0.485865:0.474600:0.491102:0.474600:0.491102:0.465019:0.485865:0.465019:0.000000 , existen :@0.491054:0.471428:0.553558:0.471428:0.553558:0.454994:0.491054:0.454994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A, B, C, D:@0.553418:0.471428:0.612568:0.471428:0.612568:0.455022:0.553418:0.455022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 puntos del plano, tales que::@0.612561:0.471428:0.816093:0.471428:0.816093:0.454994:0.612561:0.454994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB:@0.492159:0.498790:0.510805:0.498790:0.510805:0.482384:0.492159:0.482384:0.000000:0.000000 :@0.510750:0.498790:0.547178:0.498790:0.547178:0.482356:0.510750:0.482356:0.000000:0.000000:0.000000:0.000000:0.000000 5 5:@0.514708:0.498235:0.562438:0.498235:0.562438:0.484519:0.514708:0.484519:0.000000:0.000000:0.000000 u:@0.533907:0.498790:0.543221:0.498790:0.543221:0.482384:0.533907:0.482384:0.000000 5:@0.562346:0.499372:0.566432:0.499372:0.566432:0.481718:0.562346:0.481718:0.000000 ( , )І ( , ) :@0.566340:0.498790:0.669396:0.498791:0.669396:0.482357:0.566340:0.482356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.571144:0.498790:0.602044:0.498791:0.602044:0.482385:0.571144:0.482384:0.000000:0.000000:0.000000 1:@0.580951:0.501963:0.586187:0.501963:0.586187:0.492382:0.580951:0.492382:0.000000 1:@0.601982:0.501963:0.607218:0.501963:0.607218:0.492382:0.601982:0.492382:0.000000 A B:@0.624512:0.498791:0.655433:0.498791:0.655433:0.482385:0.624512:0.482385:0.000000:0.000000:0.000000 1:@0.634338:0.501963:0.639575:0.501963:0.639575:0.492382:0.634338:0.492382:0.000000 1:@0.655371:0.501963:0.660608:0.501963:0.660608:0.492382:0.655371:0.492382:0.000000 , :@0.669304:0.499374:0.689147:0.499374:0.689147:0.481719:0.669304:0.481719:0.000000:0.000000 ( , ):@0.689055:0.498791:0.724378:0.498791:0.724378:0.482357:0.689055:0.482357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.693859:0.498791:0.719574:0.498791:0.719574:0.482385:0.693859:0.482385:0.000000:0.000000:0.000000 6:@0.724305:0.499374:0.728391:0.499374:0.728391:0.481719:0.724305:0.481719:0.000000 CD:@0.487532:0.526153:0.508884:0.526153:0.508884:0.509747:0.487532:0.509747:0.000000:0.000000 :@0.508829:0.526153:0.543681:0.526154:0.543681:0.509720:0.508829:0.509719:0.000000:0.000000:0.000000:0.000000:0.000000 5 5:@0.512787:0.525598:0.558940:0.525600:0.558940:0.511884:0.512787:0.511883:0.000000:0.000000:0.000000 v:@0.531992:0.526154:0.539723:0.526154:0.539723:0.509748:0.531992:0.509748:0.000000 5:@0.558848:0.526737:0.562935:0.526737:0.562935:0.509083:0.558848:0.509083:0.000000 ( , )І ( , ) :@0.562843:0.526154:0.671310:0.526154:0.671310:0.509720:0.562843:0.509720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C D:@0.567647:0.526154:0.601252:0.526154:0.601252:0.509748:0.567647:0.509748:0.000000:0.000000:0.000000 1:@0.577472:0.529327:0.582708:0.529327:0.582708:0.519746:0.577472:0.519746:0.000000 1:@0.601190:0.529327:0.606427:0.529327:0.606427:0.519746:0.601190:0.519746:0.000000 C D:@0.623721:0.526154:0.657347:0.526154:0.657347:0.509748:0.623721:0.509748:0.000000:0.000000:0.000000 1:@0.633565:0.529327:0.638802:0.529327:0.638802:0.519746:0.633565:0.519746:0.000000 1:@0.657285:0.529327:0.662522:0.529327:0.662522:0.519746:0.657285:0.519746:0.000000 , :@0.671218:0.526737:0.691061:0.526737:0.691061:0.509083:0.671218:0.509083:0.000000:0.000000 ( , ):@0.690969:0.526154:0.728998:0.526154:0.728998:0.509720:0.690969:0.509720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C D:@0.695773:0.526154:0.724194:0.526154:0.724194:0.509748:0.695773:0.509748:0.000000:0.000000:0.000000 6:@0.728925:0.526737:0.733011:0.526737:0.733011:0.509083:0.728925:0.509083:0.000000 En la Figura 2.2. se muestran el vector y tres bipuntos equipolentes con el bipunto ( , :@0.293648:0.553516:0.930926:0.553516:0.930926:0.537082:0.293648:0.537082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.571745:0.553516:0.579476:0.553516:0.579476:0.537110:0.571745:0.537110:0.000000 A:@0.913862:0.553516:0.923747:0.553516:0.923747:0.537110:0.913862:0.537110:0.000000 B:@0.293648:0.570158:0.302484:0.570158:0.302484:0.553752:0.293648:0.553752:0.000000 ) con :@0.302410:0.570158:0.342851:0.570158:0.342851:0.553724:0.302410:0.553724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB:@0.342741:0.570158:0.361387:0.570158:0.361387:0.553752:0.342741:0.553752:0.000000:0.000000 .:@0.361332:0.570158:0.396932:0.570158:0.396932:0.553724:0.361332:0.553724:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.365289:0.569603:0.380623:0.569603:0.380623:0.555888:0.365289:0.555888:0.000000 u:@0.384488:0.570158:0.393802:0.570158:0.393802:0.553752:0.384488:0.553752:0.000000 B:@0.749504:0.607810:0.758340:0.607810:0.758340:0.591404:0.749504:0.591404:0.000000 2:@0.758269:0.610988:0.763506:0.610988:0.763506:0.601407:0.758269:0.601407:0.000000 A:@0.642774:0.658562:0.652658:0.658562:0.652658:0.642155:0.642774:0.642155:0.000000 2:@0.652592:0.661734:0.657828:0.661734:0.657828:0.652153:0.652592:0.652153:0.000000 B:@0.673199:0.609730:0.682035:0.609730:0.682035:0.593324:0.673199:0.593324:0.000000 1:@0.681970:0.612903:0.687206:0.612903:0.687206:0.603322:0.681970:0.603322:0.000000 A:@0.566472:0.660478:0.576357:0.660478:0.576357:0.644072:0.566472:0.644072:0.000000 1:@0.576290:0.663650:0.581527:0.663650:0.581527:0.654069:0.576290:0.654069:0.000000 AB:@0.493980:0.620487:0.512626:0.620487:0.512626:0.604081:0.493980:0.604081:0.000000:0.000000 u:@0.404566:0.633136:0.413880:0.633136:0.413880:0.616730:0.404566:0.616730:0.000000 B:@0.578737:0.611209:0.587572:0.611209:0.587572:0.594803:0.578737:0.594803:0.000000 A:@0.472008:0.661957:0.481893:0.661957:0.481893:0.645551:0.472008:0.645551:0.000000 B:@0.819646:0.607993:0.828481:0.607993:0.828481:0.591587:0.819646:0.591587:0.000000 3:@0.828414:0.611165:0.833651:0.611165:0.833651:0.601584:0.828414:0.601584:0.000000 A:@0.712917:0.658741:0.722802:0.658741:0.722802:0.642334:0.712917:0.642334:0.000000 3:@0.722737:0.661913:0.727973:0.661913:0.727973:0.652332:0.722737:0.652332:0.000000 Figura 2.2.:@0.573800:0.694464:0.646833:0.694464:0.646833:0.678030:0.573800:0.678030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En la Figura 2.3. se muestran el vector y dos puntos equipolentes (C, ) del vector :@0.293660:0.721827:0.930958:0.721827:0.930958:0.705393:0.293660:0.705393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.584384:0.721827:0.593698:0.721827:0.593698:0.705421:0.584384:0.705421:0.000000 D:@0.829753:0.721827:0.841276:0.721827:0.841276:0.705421:0.829753:0.705421:0.000000 :@0.926906:0.721827:0.930938:0.721827:0.930938:0.705393:0.926906:0.705393:0.000000 CD:@0.293660:0.738469:0.315013:0.738469:0.315013:0.722063:0.293660:0.722063:0.000000:0.000000 .:@0.314957:0.738469:0.348974:0.738469:0.348974:0.722035:0.314957:0.722035:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.318915:0.737914:0.334248:0.737914:0.334248:0.724198:0.318915:0.724198:0.000000 v:@0.338114:0.738469:0.345845:0.738469:0.345845:0.722063:0.338114:0.722063:0.000000 Figura 2.3.:@0.573819:0.862353:0.646851:0.862353:0.646851:0.845920:0.573819:0.845920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 D:@0.481101:0.783152:0.492624:0.783152:0.492624:0.766746:0.481101:0.766746:0.000000 C:@0.584108:0.840622:0.594011:0.840622:0.594011:0.824216:0.584108:0.824216:0.000000 C:@0.704584:0.830678:0.714487:0.830678:0.714487:0.814272:0.704584:0.814272:0.000000 1:@0.714398:0.833857:0.719635:0.833857:0.719635:0.824276:0.714398:0.824276:0.000000 D:@0.589769:0.769880:0.601292:0.769880:0.601292:0.753474:0.589769:0.753474:0.000000 1:@0.601227:0.773053:0.606464:0.773053:0.606464:0.763472:0.601227:0.763472:0.000000 CD:@0.512880:0.807951:0.534141:0.807951:0.534141:0.791545:0.512880:0.791545:0.000000:0.000000 v:@0.443632:0.815814:0.451363:0.815814:0.451363:0.799408:0.443632:0.799408:0.000000 C:@0.792552:0.830634:0.802455:0.830634:0.802455:0.814228:0.792552:0.814228:0.000000 2:@0.802390:0.833807:0.807627:0.833807:0.807627:0.824226:0.802390:0.824226:0.000000 D:@0.676575:0.769830:0.688097:0.769830:0.688097:0.753424:0.676575:0.753424:0.000000 2:@0.688032:0.773002:0.693269:0.773002:0.693269:0.763421:0.688032:0.763421:0.000000 En la suma , se elige un representante de ; por ejemplo ( , ), y a partir del punto :@0.293660:0.889714:0.931058:0.889714:0.931058:0.873280:0.293660:0.873280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.374607:0.889714:0.383921:0.889714:0.383921:0.873308:0.374607:0.873308:0.000000 1:@0.387455:0.889159:0.402788:0.889159:0.402788:0.875444:0.387455:0.875444:0.000000 v:@0.406304:0.889714:0.414035:0.889714:0.414035:0.873308:0.406304:0.873308:0.000000 u:@0.629326:0.889714:0.638641:0.889714:0.638641:0.873308:0.629326:0.873308:0.000000 A B:@0.742605:0.889714:0.773179:0.889714:0.773179:0.873308:0.742605:0.873308:0.000000:0.000000:0.000000 1:@0.752436:0.892886:0.757673:0.892886:0.757673:0.883305:0.752436:0.883305:0.000000 1:@0.773122:0.892886:0.778359:0.892886:0.778359:0.883305:0.773122:0.883305:0.000000 B:@0.293667:0.906356:0.302502:0.906356:0.302502:0.889950:0.293667:0.889950:0.000000 1:@0.302601:0.909529:0.307838:0.909529:0.307838:0.899948:0.302601:0.899948:0.000000 se construye el punto , de modo que ( , ) :@0.307914:0.906357:0.667722:0.906357:0.667722:0.889923:0.307914:0.889923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.482599:0.906357:0.492502:0.906357:0.492502:0.889950:0.482599:0.889950:0.000000 1:@0.492619:0.909529:0.497856:0.909529:0.497856:0.899948:0.492619:0.899948:0.000000 B C:@0.620560:0.906357:0.653266:0.906357:0.653266:0.889950:0.620560:0.889950:0.000000:0.000000:0.000000 1:@0.629509:0.909529:0.634746:0.909529:0.634746:0.899948:0.629509:0.899948:0.000000 1:@0.653373:0.909529:0.658610:0.909529:0.658610:0.899948:0.653373:0.899948:0.000000 [:@0.668900:0.906218:0.684234:0.906218:0.684234:0.892169:0.668900:0.892169:0.000000 CD:@0.684381:0.906357:0.705917:0.906357:0.705917:0.889950:0.684381:0.889950:0.000000:0.000000 . El bipunto ( , ) es un :@0.706028:0.906357:0.930939:0.906357:0.930939:0.889923:0.706028:0.889923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.711237:0.905802:0.726570:0.905802:0.726570:0.892086:0.711237:0.892086:0.000000 v:@0.731927:0.906357:0.739658:0.906357:0.739658:0.889950:0.731927:0.889950:0.000000 A C:@0.836500:0.906357:0.870244:0.906357:0.870244:0.889950:0.836500:0.889950:0.000000:0.000000:0.000000 1:@0.846487:0.909529:0.851724:0.909529:0.851724:0.899948:0.846487:0.899948:0.000000 1:@0.870351:0.909529:0.875588:0.909529:0.875588:0.899948:0.870351:0.899948:0.000000 representante del vector :@0.293662:0.922998:0.475667:0.922998:0.475667:0.906565:0.293662:0.906565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AC:@0.475470:0.922998:0.494871:0.922998:0.494871:0.906592:0.475470:0.906592:0.000000:0.000000 .:@0.494816:0.922998:0.561230:0.922998:0.561230:0.906565:0.494816:0.906565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 1:@0.498774:0.922444:0.546504:0.922444:0.546504:0.908728:0.498774:0.908728:0.000000:0.000000:0.000000 u:@0.517973:0.922998:0.527287:0.922998:0.527287:0.906592:0.517973:0.906592:0.000000 v:@0.550369:0.922998:0.558100:0.922998:0.558100:0.906592:0.550369:0.906592:0.000000 Tema 2. Operaciones con vectores en el plano:@0.073089:0.098522:0.744746:0.098522:0.744746:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si un bote en reposo, recibe el empuje de la corriente :@0.292999:0.165426:0.675969:0.165426:0.675969:0.148992:0.292999:0.148992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del agua y del viento, ¿cuál será su dirección en ese :@0.292999:0.182068:0.676012:0.182068:0.676012:0.165634:0.292999:0.165634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 momento?:@0.292999:0.198710:0.373597:0.198710:0.373597:0.182276:0.292999:0.182276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aprende la siguiente :@0.082305:0.794230:0.219561:0.794230:0.219561:0.779290:0.082305:0.779290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 simbología matemática::@0.082305:0.809359:0.237567:0.809359:0.237567:0.794419:0.082305:0.794419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A la suma de dos :@0.082305:0.824488:0.195945:0.824488:0.195945:0.809548:0.082305:0.809548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vectores y la :@0.082305:0.839617:0.186474:0.839617:0.186474:0.824677:0.082305:0.824677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.140104:0.839617:0.168702:0.839617:0.168702:0.824702:0.140104:0.824702:0.000000:0.000000:0.000000:0.000000 denotamos con + .:@0.082305:0.854746:0.222836:0.854746:0.222836:0.839806:0.082305:0.839806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.188314:0.854746:0.220159:0.854746:0.220159:0.839831:0.188314:0.839831:0.000000:0.000000:0.000000 Simbología :@0.087319:0.762424:0.181137:0.762424:0.181137:0.745477:0.087319:0.745477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.087319:0.779066:0.180984:0.779066:0.180984:0.762119:0.087319:0.762119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dirección de :@0.682542:0.139353:0.778567:0.139353:0.778567:0.122919:0.682542:0.122919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la corriente:@0.692795:0.155995:0.774519:0.155995:0.774519:0.139561:0.692795:0.139561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dirección del viento:@0.735279:0.206114:0.880941:0.206114:0.880941:0.189680:0.735279:0.189680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 bote:@0.735279:0.180888:0.769511:0.180888:0.769511:0.164454:0.735279:0.164454:0.000000:0.000000:0.000000:0.000000 Figura 2.1.:@0.128207:0.620732:0.201240:0.620732:0.201240:0.604298:0.128207:0.604298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.205504:0.434421:0.213235:0.434421:0.213235:0.418015:0.205504:0.418015:0.000000 u:@0.104534:0.424236:0.113848:0.424236:0.113848:0.407830:0.104534:0.407830:0.000000 v:@0.202211:0.519383:0.209942:0.519383:0.209942:0.502977:0.202211:0.502977:0.000000 AC:@0.085217:0.550397:0.104618:0.550397:0.104618:0.533991:0.085217:0.533991:0.000000:0.000000 AB:@0.182803:0.578329:0.201450:0.578329:0.201450:0.561923:0.182803:0.561923:0.000000:0.000000 BC:@0.154342:0.531156:0.173007:0.531156:0.173007:0.514750:0.154342:0.514750:0.000000:0.000000 u:@0.146754:0.571540:0.156068:0.571540:0.156068:0.555134:0.146754:0.555134:0.000000 v:@0.151496:0.550397:0.159227:0.550397:0.159227:0.533991:0.151496:0.533991:0.000000 u:@0.123984:0.550397:0.133298:0.550397:0.133298:0.533991:0.123984:0.533991:0.000000 C:@0.114572:0.496526:0.123575:0.496526:0.123575:0.481611:0.114572:0.481611:0.000000 B:@0.241857:0.542250:0.249889:0.542250:0.249889:0.527336:0.241857:0.527336:0.000000 5:@0.104623:0.549575:0.118562:0.549575:0.118562:0.537106:0.104623:0.537106:0.000000 1:@0.136517:0.549575:0.150457:0.549575:0.150457:0.537106:0.136517:0.537106:0.000000 A:@0.107635:0.594975:0.116621:0.594975:0.116621:0.580060:0.107635:0.580060:0.000000 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