133:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.º BG:@0.837761:0.967458:0.879897:0.967458:0.879897:0.954794:0.837761:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.:@0.096359:0.681695:0.110585:0.681695:0.110585:0.664794:0.096359:0.664794:0.000000:0.000000
  Sean los vectores   = (1,   + 2);   = (  –1, 1) y   = (1, –1);:@0.110585:0.681695:0.532834:0.681695:0.532834:0.665306:0.110585:0.665306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.255351:0.681695:0.265247:0.681695:0.265247:0.665334:0.255351:0.665334:0.000000
a:@0.305419:0.681695:0.314688:0.681695:0.314688:0.665334:0.305419:0.665334:0.000000
B:@0.354860:0.681695:0.363705:0.681695:0.363705:0.665334:0.354860:0.665334:0.000000
b:@0.387643:0.681695:0.396912:0.681695:0.396912:0.665334:0.387643:0.665334:0.000000
C:@0.456452:0.681695:0.466366:0.681695:0.466366:0.665334:0.456452:0.665334:0.000000
 :@0.096359:0.701859:0.100395:0.701859:0.100395:0.685470:0.096359:0.685470:0.000000
sabiendo que   +   – 2  = 2  + 3 .:@0.124848:0.701859:0.370249:0.701859:0.370249:0.685470:0.124848:0.685470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.229536:0.701859:0.239431:0.701859:0.239431:0.685498:0.229536:0.685498:0.000000
B:@0.258485:0.701859:0.267331:0.701859:0.267331:0.685498:0.258485:0.685498:0.000000
C:@0.293609:0.701859:0.303523:0.701859:0.303523:0.685498:0.293609:0.685498:0.000000
i:@0.331569:0.701859:0.335366:0.701859:0.335366:0.685498:0.331569:0.685498:0.000000
j:@0.363412:0.701859:0.367043:0.701859:0.367043:0.685498:0.363412:0.685498:0.000000
Determinemos  y  .:@0.124848:0.722024:0.277392:0.722024:0.277392:0.705635:0.124848:0.705635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.239468:0.722024:0.274186:0.722024:0.274186:0.705663:0.239468:0.705663:0.000000:0.000000:0.000000
Paso 1. :@0.102121:0.264741:0.157756:0.264741:0.157756:0.249163:0.102121:0.249163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si tomamos el inicio del recorrido como el punto (0, 0), representemos los tres :@0.157756:0.264741:0.680154:0.264741:0.680154:0.249842:0.157756:0.249842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desplazamientos como vectores.:@0.102121:0.279829:0.320368:0.279829:0.320368:0.264930:0.102121:0.264930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8 km al norte = (0, 8); 6 km al este = (6, 0) y 5 km al sur = (0, –5):@0.102121:0.302045:0.517859:0.302045:0.517859:0.287146:0.102121:0.287146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 2.:@0.102121:0.324035:0.154372:0.324035:0.154372:0.308457:0.102121:0.308457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Sumemos los tres vectores::@0.154372:0.324035:0.338729:0.324035:0.338729:0.309136:0.154372:0.309136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 8) + (6, 0) + (0, –5) = (0 + 6 + 0; 8 + 0 –5) = (6, 3) km:@0.102121:0.346252:0.460400:0.346252:0.460400:0.331353:0.102121:0.331353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1.:@0.102121:0.402990:0.154372:0.402990:0.154372:0.387412:0.102121:0.387412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Si llamamos   al vector del desplazamiento total, calculemos su módulo.:@0.154372:0.402990:0.640066:0.402990:0.640066:0.388091:0.154372:0.388091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.241568:0.402990:0.250581:0.402990:0.250581:0.388116:0.241568:0.388116:0.000000
C:@0.109283:0.429576:0.118206:0.429576:0.118206:0.414851:0.109283:0.414851:0.000000
km:@0.273573:0.429576:0.293482:0.429576:0.293482:0.414851:0.273573:0.414851:0.000000:0.000000
:@0.110272:0.419411:0.118681:0.419411:0.118681:0.404960:0.110272:0.404960:0.000000:0.000000
=:@0.127470:0.430186:0.136575:0.430186:0.136575:0.416170:0.127470:0.416170:0.000000
+:@0.167987:0.430186:0.177092:0.430186:0.177092:0.416170:0.167987:0.416170:0.000000
=:@0.198105:0.430186:0.207210:0.430186:0.207210:0.416170:0.198105:0.416170:0.000000
=:@0.241408:0.430186:0.250513:0.430186:0.250513:0.416170:0.241408:0.416170:0.000000
6:@0.150705:0.429576:0.158799:0.429576:0.158799:0.414826:0.150705:0.414826:0.000000
3:@0.179447:0.429576:0.187540:0.429576:0.187540:0.414826:0.179447:0.414826:0.000000
45 67:@0.221622:0.429576:0.273865:0.429576:0.273865:0.414826:0.221622:0.414826:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.159085:0.422680:0.163775:0.422680:0.163775:0.414132:0.159085:0.414132:0.000000
2:@0.187305:0.422680:0.191995:0.422680:0.191995:0.414132:0.187305:0.414132:0.000000
,:@0.261657:0.429576:0.264542:0.429576:0.264542:0.414826:0.261657:0.414826:0.000000
Paso 1.:@0.102121:0.746216:0.154372:0.746216:0.154372:0.730638:0.102121:0.730638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 El vector 2  + 3  lo expresamos como: (2, 3):@0.154372:0.746216:0.440332:0.746216:0.440332:0.731317:0.154372:0.731317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.227025:0.746216:0.230476:0.746216:0.230476:0.731342:0.227025:0.731342:0.000000
j:@0.255974:0.746216:0.259274:0.746216:0.259274:0.731342:0.255974:0.731342:0.000000
Sumamos:   +   – 2  = 2  + 3 ;:@0.102121:0.768432:0.303502:0.768432:0.303502:0.753533:0.102121:0.753533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.175581:0.768432:0.184577:0.768432:0.184577:0.753558:0.175581:0.753558:0.000000
B:@0.201899:0.768432:0.209940:0.768432:0.209940:0.753558:0.201899:0.753558:0.000000
C:@0.233829:0.768432:0.242841:0.768432:0.242841:0.753558:0.233829:0.753558:0.000000
i:@0.268339:0.768432:0.271790:0.768432:0.271790:0.753558:0.268339:0.753558:0.000000
j:@0.297287:0.768432:0.300587:0.768432:0.300587:0.753558:0.297287:0.753558:0.000000
(1,   + 2) + (  –1, 1) –2(1, –1) =(2, 3):@0.102121:0.790649:0.335164:0.790649:0.335164:0.775750:0.102121:0.775750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.121320:0.790649:0.129746:0.790649:0.129746:0.775775:0.121320:0.775775:0.000000
b:@0.181444:0.790649:0.189870:0.790649:0.189870:0.775775:0.181444:0.775775:0.000000
(1 +   –1 –2,   + 2 + 1 + 2) = (2, 3):@0.102121:0.812865:0.326000:0.812865:0.326000:0.797966:0.102121:0.797966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.132058:0.812865:0.140484:0.812865:0.140484:0.797991:0.132058:0.797991:0.000000
a:@0.187508:0.812865:0.195935:0.812865:0.195935:0.797991:0.187508:0.797991:0.000000
(  –2,   + 5) = (2, 3):@0.102121:0.835082:0.229289:0.835082:0.229289:0.820183:0.102121:0.820183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.106561:0.835082:0.114987:0.835082:0.114987:0.820208:0.106561:0.820208:0.000000
a:@0.141791:0.835082:0.150217:0.835082:0.150217:0.820208:0.141791:0.820208:0.000000
Paso 2.:@0.102121:0.860052:0.154372:0.860052:0.154372:0.844474:0.102121:0.844474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Por la igualdad de vectores tenemos los valores de   y  .:@0.154372:0.860052:0.532519:0.860052:0.532519:0.845153:0.154372:0.845153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.498042:0.860052:0.529604:0.860052:0.529604:0.845178:0.498042:0.845178:0.000000:0.000000:0.000000
b:@0.102121:0.882268:0.110548:0.882268:0.110548:0.867394:0.102121:0.867394:0.000000
 – 2 = 2 entonces:   = 4,   + 5 = 3 entonces   = –2:@0.110548:0.882268:0.443582:0.882268:0.443582:0.867369:0.110548:0.867369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.232101:0.882268:0.240528:0.882268:0.240528:0.867394:0.232101:0.867394:0.000000
a:@0.272609:0.882268:0.281035:0.882268:0.281035:0.867394:0.272609:0.867394:0.000000
a:@0.401282:0.882268:0.409709:0.882268:0.409709:0.867394:0.401282:0.867394:0.000000
Paso 1.:@0.102121:0.516171:0.154372:0.516171:0.154372:0.500593:0.102121:0.500593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Hallemos 3:@0.154372:0.516171:0.232153:0.516171:0.232153:0.501272:0.154372:0.501272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.232153:0.516171:0.240446:0.516171:0.240446:0.501297:0.232153:0.501297:0.000000
3:@0.102121:0.545400:0.110215:0.545400:0.110215:0.531297:0.102121:0.531297:0.000000
3:@0.133119:0.545400:0.141212:0.545400:0.141212:0.531297:0.133119:0.531297:0.000000
5 2:@0.149471:0.537731:0.176920:0.537731:0.176920:0.523629:0.149471:0.523629:0.000000:0.000000:0.000000
3 3:@0.149471:0.555233:0.177101:0.555233:0.177101:0.541130:0.149471:0.541130:0.000000:0.000000:0.000000
,:@0.159687:0.545400:0.162573:0.545400:0.162573:0.531297:0.159687:0.531297:0.000000
.:@0.163402:0.545400:0.166288:0.545400:0.166288:0.531297:0.163402:0.531297:0.000000
3:@0.204864:0.545400:0.212957:0.545400:0.212957:0.531297:0.204864:0.531297:0.000000
5:@0.221069:0.537720:0.229162:0.537720:0.229162:0.523617:0.221069:0.523617:0.000000
3:@0.221069:0.555220:0.229162:0.555220:0.229162:0.541118:0.221069:0.541118:0.000000
, 3:@0.231302:0.545387:0.245847:0.545387:0.245847:0.531284:0.231302:0.531284:0.000000:0.000000:0.000000
.:@0.235017:0.545387:0.237902:0.545387:0.237902:0.531284:0.235017:0.531284:0.000000
2:@0.253955:0.537707:0.262049:0.537707:0.262049:0.523605:0.253955:0.523605:0.000000
3:@0.254138:0.555208:0.262231:0.555208:0.262231:0.541105:0.254138:0.541105:0.000000
5, 2:@0.289331:0.545374:0.311754:0.545374:0.311754:0.531272:0.289331:0.531272:0.000000:0.000000:0.000000:0.000000
.:@0.300924:0.545374:0.303810:0.545374:0.303810:0.531272:0.300924:0.531272:0.000000
(:@0.283565:0.548218:0.289088:0.548218:0.289088:0.530278:0.283565:0.530278:0.000000
):@0.311925:0.548218:0.317448:0.548218:0.317448:0.530278:0.311925:0.530278:0.000000
= ⎜:@0.121722:0.546009:0.147694:0.547142:0.147694:0.533127:0.121722:0.531994:0.000000:0.000000:0.000000
⎛:@0.141326:0.537345:0.147694:0.537345:0.147694:0.523330:0.141326:0.523330:0.000000
⎝:@0.141326:0.555481:0.147694:0.555481:0.147694:0.541465:0.141326:0.541465:0.000000
⎞ ⎛:@0.178741:0.537345:0.204430:0.537345:0.204430:0.523330:0.178741:0.523330:0.000000:0.000000:0.000000
⎠ ⎝:@0.178741:0.555481:0.204430:0.555481:0.204430:0.541465:0.178741:0.541465:0.000000:0.000000:0.000000
⎟=⎜:@0.178741:0.547142:0.204430:0.547142:0.204430:0.533127:0.178741:0.533127:0.000000:0.000000:0.000000
⋅:@0.214033:0.546010:0.218179:0.546010:0.218179:0.531994:0.214033:0.531994:0.000000
⋅ ⎟=:@0.246921:0.546010:0.281285:0.546010:0.281285:0.531994:0.246921:0.531994:0.000000:0.000000:0.000000:0.000000
⎞:@0.263888:0.537345:0.270257:0.537345:0.270257:0.523330:0.263888:0.523330:0.000000
⎠:@0.263888:0.555481:0.270257:0.555481:0.270257:0.541465:0.263888:0.541465:0.000000
V:@0.108969:0.545400:0.117178:0.545400:0.117178:0.531546:0.108969:0.531546:0.000000
Paso 2.:@0.102121:0.582071:0.154372:0.582071:0.154372:0.566493:0.102121:0.566493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Sumemos los tres vectores.:@0.154372:0.582071:0.338545:0.582071:0.338545:0.567172:0.154372:0.567172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3 –:@0.125307:0.605121:0.153054:0.605121:0.153054:0.591019:0.125307:0.591019:0.000000:0.000000:0.000000
4, 3:@0.190071:0.605121:0.213555:0.605121:0.213555:0.591019:0.190071:0.591019:0.000000:0.000000:0.000000:0.000000
.:@0.202725:0.605121:0.205611:0.605121:0.205611:0.591019:0.202725:0.591019:0.000000
5, 2 – –3, –1:@0.237122:0.605121:0.327012:0.605121:0.327012:0.591019:0.237122:0.591019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.248715:0.605121:0.251601:0.605121:0.251601:0.591019:0.248715:0.591019:0.000000
.:@0.304042:0.605121:0.306928:0.605121:0.306928:0.591019:0.304042:0.591019:0.000000
3 –:@0.125340:0.626618:0.153087:0.626618:0.153087:0.612515:0.125340:0.612515:0.000000:0.000000:0.000000
4 5– –3 , 3 2– –1:@0.190104:0.626618:0.330545:0.626618:0.330545:0.612515:0.190104:0.612515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.264471:0.626618:0.267357:0.626618:0.267357:0.612515:0.264471:0.612515:0.000000
(:@0.183634:0.630571:0.189157:0.630571:0.189157:0.610389:0.183634:0.610389:0.000000
):@0.334025:0.630571:0.339548:0.630571:0.339548:0.610389:0.334025:0.610389:0.000000
(:@0.183634:0.607945:0.189157:0.607945:0.189157:0.590005:0.183634:0.590005:0.000000
) (:@0.213304:0.607945:0.236822:0.607945:0.236822:0.590005:0.213304:0.590005:0.000000:0.000000:0.000000
) (:@0.259659:0.607945:0.283508:0.607945:0.283508:0.590005:0.259659:0.590005:0.000000:0.000000:0.000000
):@0.324672:0.607945:0.330194:0.607945:0.330194:0.590005:0.324672:0.590005:0.000000
( ):@0.231598:0.629445:0.259394:0.629445:0.259394:0.611505:0.231598:0.611505:0.000000:0.000000:0.000000
( ):@0.308004:0.629445:0.333727:0.629445:0.333727:0.611505:0.308004:0.611505:0.000000:0.000000:0.000000
+:@0.114372:0.605736:0.123477:0.605736:0.123477:0.591721:0.114372:0.591721:0.000000
=:@0.172220:0.605736:0.181325:0.605736:0.181325:0.591721:0.172220:0.591721:0.000000
+:@0.220366:0.605736:0.229471:0.605736:0.229471:0.591721:0.220366:0.591721:0.000000
+:@0.114372:0.627233:0.123477:0.627233:0.123477:0.613217:0.114372:0.613217:0.000000
=:@0.172220:0.627233:0.181325:0.627233:0.181325:0.613217:0.172220:0.613217:0.000000
+:@0.200249:0.627233:0.209354:0.627233:0.209354:0.613217:0.200249:0.613217:0.000000
+:@0.276290:0.627233:0.285395:0.627233:0.285395:0.613217:0.276290:0.613217:0.000000
U:@0.102132:0.605126:0.112083:0.605126:0.112083:0.591273:0.102132:0.591273:0.000000
V W:@0.132135:0.605126:0.167992:0.605126:0.167992:0.591273:0.132135:0.591273:0.000000:0.000000:0.000000
U:@0.102132:0.626622:0.112083:0.626622:0.112083:0.612769:0.102132:0.612769:0.000000
V W:@0.132135:0.626622:0.167992:0.626622:0.167992:0.612769:0.132135:0.612769:0.000000:0.000000:0.000000
3 –:@0.125319:0.648816:0.153065:0.648816:0.153065:0.634714:0.125319:0.634714:0.000000:0.000000:0.000000
+:@0.114373:0.649426:0.123478:0.649426:0.123478:0.635411:0.114373:0.635411:0.000000
=:@0.172221:0.649426:0.181326:0.649426:0.181326:0.635411:0.172221:0.635411:0.000000
U:@0.102117:0.648816:0.112068:0.648816:0.112068:0.634963:0.102117:0.634963:0.000000
V W:@0.132119:0.648816:0.167975:0.648816:0.167975:0.634963:0.132119:0.634963:0.000000:0.000000:0.000000
12, 6:@0.187777:0.648953:0.218576:0.648953:0.218576:0.634850:0.187777:0.634850:0.000000:0.000000:0.000000:0.000000:0.000000
cción y expresión:@0.117728:0.158808:0.242599:0.158808:0.242599:0.143444:0.117728:0.143444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.096132:0.159594:0.108221:0.159594:0.108221:0.142458:0.096132:0.142458:0.000000
Ejemplos paso a paso:@0.096359:0.184907:0.251252:0.184907:0.251252:0.169543:0.096359:0.169543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.096359:0.212510:0.110585:0.212510:0.110585:0.195610:0.096359:0.195610:0.000000:0.000000
  Respondamos a la pregunta del problema inicial. :@0.110585:0.212510:0.486522:0.212510:0.486522:0.196121:0.110585:0.196121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.124848:0.239797:0.139756:0.239797:0.139756:0.222897:0.124848:0.222897:0.000000:0.000000
  Hallemos el desplazamiento total del camión:@0.139756:0.239797:0.483502:0.239797:0.483502:0.223409:0.139756:0.223409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.124848:0.378764:0.141065:0.378764:0.141065:0.361864:0.124848:0.361864:0.000000:0.000000
  ¿A qué distancia desde su punto de partida se encuentra el camión?:@0.141065:0.378764:0.653403:0.378764:0.653403:0.362376:0.141065:0.362376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para el vector :@0.096359:0.099904:0.198557:0.099904:0.198557:0.083515:0.096359:0.083515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.199778:0.099974:0.209674:0.099974:0.209674:0.083613:0.199778:0.083613:0.000000
a a:@0.231031:0.099974:0.263906:0.099974:0.263906:0.083613:0.231031:0.083613:0.000000:0.000000:0.000000
:@0.200349:0.088675:0.207905:0.088675:0.207905:0.072618:0.200349:0.072618:0.000000
=:@0.212813:0.100652:0.222930:0.100652:0.222930:0.085079:0.212813:0.085079:0.000000
(, :@0.225535:0.099974:0.254647:0.099974:0.254647:0.083585:0.225535:0.083585:0.000000:0.000000:0.000000
) y el escalar :@0.271033:0.099974:0.363060:0.099894:0.363060:0.083505:0.271033:0.083585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.239146:0.101978:0.244358:0.101978:0.244358:0.092480:0.239146:0.092480:0.000000
2:@0.263443:0.101978:0.268654:0.101978:0.268654:0.092480:0.263443:0.092480:0.000000
r:@0.365572:0.100153:0.370860:0.100153:0.370860:0.083792:0.365572:0.083792:0.000000
∈:@0.373680:0.100831:0.386819:0.100831:0.386819:0.085258:0.373680:0.085258:0.000000
:@0.388440:0.103168:0.401745:0.103168:0.401745:0.082754:0.388440:0.082754:0.000000
, el producto escalar se define como::@0.401939:0.099894:0.669765:0.099894:0.669765:0.083505:0.401939:0.083505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rA ra a:@0.098872:0.126132:0.185463:0.126132:0.185463:0.109771:0.098872:0.109771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rara:@0.218394:0.126132:0.261643:0.126132:0.261643:0.109771:0.218394:0.109771:0.000000:0.000000:0.000000:0.000000
⋅=:@0.107515:0.126810:0.137846:0.126810:0.137846:0.111237:0.107515:0.111237:0.000000:0.000000
=:@0.200445:0.126810:0.210562:0.126810:0.210562:0.111237:0.200445:0.111237:0.000000
:@0.115258:0.114839:0.122813:0.114839:0.122813:0.098782:0.115258:0.098782:0.000000
(,:@0.147087:0.126132:0.169661:0.126132:0.169661:0.109744:0.147087:0.109744:0.000000:0.000000
)(:@0.192585:0.126132:0.218052:0.126132:0.218052:0.109744:0.192585:0.109744:0.000000:0.000000
,:@0.237446:0.126132:0.240652:0.126132:0.240652:0.109744:0.237446:0.109744:0.000000
):@0.268755:0.126132:0.273638:0.126132:0.273638:0.109744:0.268755:0.109744:0.000000
1:@0.160698:0.128136:0.165910:0.128136:0.165910:0.118638:0.160698:0.118638:0.000000
2:@0.184994:0.128136:0.190206:0.128136:0.190206:0.118638:0.184994:0.118638:0.000000
1:@0.231686:0.128136:0.236897:0.128136:0.236897:0.118638:0.231686:0.118638:0.000000
2:@0.261162:0.128136:0.266373:0.128136:0.266373:0.118638:0.261162:0.118638:0.000000
2.:@0.096359:0.478774:0.110585:0.478774:0.110585:0.461873:0.096359:0.461873:0.000000:0.000000
  Si: :@0.110585:0.478774:0.144492:0.478774:0.144492:0.462385:0.110585:0.462385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4, 3:@0.178891:0.478922:0.204948:0.478922:0.204948:0.463253:0.178891:0.463253:0.000000:0.000000:0.000000:0.000000
.:@0.192915:0.478922:0.196121:0.478922:0.196121:0.463253:0.192915:0.463253:0.000000
...:@0.211508:0.478922:0.220796:0.478922:0.220796:0.463253:0.211508:0.463253:0.000000:0.000000:0.000000
5 2:@0.255698:0.470403:0.286195:0.470403:0.286195:0.454733:0.255698:0.454733:0.000000:0.000000:0.000000
3 3:@0.255698:0.489848:0.286398:0.489848:0.286398:0.474178:0.255698:0.474178:0.000000:0.000000:0.000000
,:@0.267049:0.478922:0.270256:0.478922:0.270256:0.463253:0.267049:0.463253:0.000000
.:@0.271177:0.478922:0.274383:0.478922:0.274383:0.463253:0.271177:0.463253:0.000000
.....:@0.295409:0.478922:0.310778:0.478922:0.310778:0.463253:0.295409:0.463253:0.000000:0.000000:0.000000:0.000000:0.000000
–3, –1 .:@0.349236:0.478922:0.404298:0.478922:0.404298:0.463253:0.349236:0.463253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.371331:0.478922:0.374538:0.478922:0.374538:0.463253:0.371331:0.463253:0.000000
(:@0.171718:0.482054:0.177854:0.482054:0.177854:0.462121:0.171718:0.462121:0.000000
):@0.204685:0.482054:0.210821:0.482054:0.210821:0.462121:0.204685:0.462121:0.000000
(:@0.342413:0.482054:0.348550:0.482054:0.348550:0.462121:0.342413:0.462121:0.000000
):@0.394287:0.482054:0.400423:0.482054:0.400423:0.462121:0.394287:0.462121:0.000000
=:@0.159050:0.479600:0.169167:0.479600:0.169167:0.464027:0.159050:0.464027:0.000000
=⎜:@0.234382:0.479600:0.253713:0.480859:0.253713:0.465286:0.234382:0.464027:0.000000:0.000000
⎛:@0.246636:0.469974:0.253713:0.469974:0.253713:0.454401:0.246636:0.454401:0.000000
⎝:@0.246636:0.490125:0.253713:0.490125:0.253713:0.474552:0.246636:0.474552:0.000000
⎞:@0.288209:0.469974:0.295285:0.469974:0.295285:0.454401:0.288209:0.454401:0.000000
⎠:@0.288209:0.490125:0.295285:0.490125:0.295285:0.474552:0.288209:0.474552:0.000000
⎟:@0.288209:0.480859:0.295285:0.480859:0.295285:0.465286:0.288209:0.465286:0.000000
=:@0.329782:0.479600:0.339899:0.479600:0.339899:0.464027:0.329782:0.464027:0.000000
U:@0.144510:0.478922:0.155567:0.478922:0.155567:0.463529:0.144510:0.463529:0.000000
V:@0.220211:0.478922:0.229333:0.478922:0.229333:0.463529:0.220211:0.463529:0.000000
W:@0.310193:0.478922:0.325064:0.478922:0.325064:0.463529:0.310193:0.463529:0.000000
 Calculemos   + 3  – :@0.404300:0.478774:0.563201:0.478774:0.563201:0.462385:0.404300:0.462385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.497691:0.478774:0.508748:0.478774:0.508748:0.462413:0.497691:0.462413:0.000000
V W:@0.536795:0.478774:0.578072:0.478774:0.578072:0.462413:0.536795:0.462413:0.000000:0.000000:0.000000
Propiedades de las :@0.755242:0.298589:0.894589:0.298589:0.894589:0.283225:0.755242:0.283225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
operaciones con :@0.755242:0.313676:0.877265:0.313676:0.877265:0.298312:0.755242:0.298312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores:@0.755242:0.328764:0.816623:0.328764:0.816623:0.313400:0.755242:0.313400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Suma::@0.755242:0.347410:0.798246:0.347410:0.798246:0.332297:0.755242:0.332297:0.000000:0.000000:0.000000:0.000000:0.000000
Conmutativa::@0.755242:0.366056:0.844751:0.366056:0.844751:0.351157:0.755242:0.351157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB BA:@0.758494:0.386825:0.836609:0.386825:0.836609:0.372100:0.758494:0.372100:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.759008:0.376656:0.835017:0.376656:0.835017:0.362204:0.759008:0.362204:0.000000:0.000000:0.000000:0.000000:0.000000
+= +:@0.769656:0.387435:0.824369:0.387435:0.824369:0.373419:0.769656:0.373419:0.000000:0.000000:0.000000:0.000000
Asociativa:@0.755242:0.407772:0.822503:0.407772:0.822503:0.392873:0.755242:0.392873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.758494:0.429660:0.767400:0.429660:0.767400:0.414935:0.758494:0.414935:0.000000
B C:@0.787468:0.429660:0.818780:0.429660:0.818780:0.414935:0.787468:0.414935:0.000000:0.000000:0.000000
A B:@0.848533:0.429660:0.879110:0.429660:0.879110:0.414935:0.848533:0.414935:0.000000:0.000000:0.000000
C:@0.899841:0.429660:0.908763:0.429660:0.908763:0.414935:0.899841:0.414935:0.000000
:@0.759019:0.419491:0.765818:0.419491:0.765818:0.405039:0.759019:0.405039:0.000000
 :@0.788374:0.419491:0.819255:0.419491:0.819255:0.405039:0.788374:0.405039:0.000000:0.000000:0.000000:0.000000
 :@0.849058:0.419491:0.878861:0.419491:0.878861:0.405039:0.849058:0.405039:0.000000:0.000000:0.000000
:@0.900852:0.419491:0.909244:0.419491:0.909244:0.405039:0.900852:0.405039:0.000000:0.000000
+:@0.769661:0.430270:0.778766:0.430270:0.778766:0.416254:0.769661:0.416254:0.000000
+:@0.798403:0.430270:0.807508:0.430270:0.807508:0.416254:0.798403:0.416254:0.000000
(:@0.781110:0.435074:0.786633:0.435074:0.786633:0.410827:0.781110:0.410827:0.000000
) (:@0.821063:0.435074:0.846705:0.435074:0.846705:0.410827:0.821063:0.410827:0.000000:0.000000:0.000000
=:@0.829451:0.430270:0.838556:0.430270:0.838556:0.416254:0.829451:0.416254:0.000000
+:@0.859701:0.430270:0.868806:0.430270:0.868806:0.416254:0.859701:0.416254:0.000000
):@0.880571:0.435074:0.886094:0.435074:0.886094:0.410827:0.880571:0.410827:0.000000
+:@0.888394:0.430270:0.897499:0.430270:0.897499:0.416254:0.888394:0.416254:0.000000
Elemento neutro:@0.755242:0.457396:0.868001:0.457396:0.868001:0.442497:0.755242:0.442497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.757362:0.477828:0.766268:0.477828:0.766268:0.463975:0.757362:0.463975:0.000000
A:@0.803915:0.477828:0.812821:0.477828:0.812821:0.463975:0.803915:0.463975:0.000000
:@0.757876:0.467671:0.718122:0.467671:0.718122:0.453220:0.757876:0.453220:0.000000
 :@0.804430:0.467671:0.787397:0.467671:0.787397:0.453220:0.804430:0.453220:0.000000:0.000000:0.000000
+=:@0.768523:0.478438:0.800300:0.478438:0.800300:0.464423:0.768523:0.464423:0.000000:0.000000
0:@0.779967:0.477828:0.788060:0.477828:0.788060:0.463726:0.779967:0.463726:0.000000
Inverso aditivo:@0.755242:0.500231:0.852457:0.500231:0.852457:0.485332:0.755242:0.485332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.757135:0.522896:0.766042:0.522896:0.766042:0.509043:0.757135:0.509043:0.000000
A:@0.796707:0.522896:0.805613:0.522896:0.805613:0.509043:0.796707:0.509043:0.000000
:@0.757650:0.512727:0.724878:0.512727:0.724878:0.498276:0.757650:0.498276:0.000000
:@0.797221:0.512727:0.764449:0.512727:0.764449:0.498276:0.797221:0.498276:0.000000
:@0.827124:0.512727:0.833923:0.512727:0.833923:0.498276:0.827124:0.498276:0.000000
+−:@0.768298:0.523506:0.795729:0.523506:0.795729:0.509491:0.768298:0.509491:0.000000:0.000000
(:@0.779751:0.528310:0.758655:0.528310:0.758655:0.504063:0.779751:0.504063:0.000000
):@0.806370:0.528310:0.785274:0.528310:0.785274:0.504063:0.806370:0.504063:0.000000
=:@0.814759:0.523506:0.823864:0.523506:0.823864:0.509491:0.814759:0.509491:0.000000
0:@0.826501:0.522896:0.834594:0.522896:0.834594:0.508794:0.826501:0.508794:0.000000
Producto por escalar::@0.755242:0.549857:0.902478:0.549857:0.902478:0.534744:0.755242:0.534744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a bA:@0.755242:0.568502:0.785531:0.568502:0.785531:0.553629:0.755242:0.553629:0.000000:0.000000:0.000000:0.000000
(:@0.763669:0.568502:0.768108:0.568502:0.768108:0.553603:0.763669:0.553603:0.000000
) = (:@0.785531:0.568502:0.811732:0.568502:0.811732:0.553603:0.785531:0.553603:0.000000:0.000000:0.000000:0.000000:0.000000
ab A b aA:@0.811732:0.568502:0.885961:0.568502:0.885961:0.553629:0.811732:0.553629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) =  (:@0.828584:0.568502:0.868539:0.568502:0.868539:0.553603:0.828584:0.553603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.885961:0.568502:0.890401:0.568502:0.890401:0.553603:0.885961:0.553603:0.000000
(  +  )  = :@0.755242:0.587148:0.824614:0.587148:0.824614:0.572249:0.755242:0.572249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.759682:0.587148:0.768108:0.587148:0.768108:0.572274:0.759682:0.572274:0.000000
b A:@0.785430:0.587148:0.807292:0.587148:0.807292:0.572274:0.785430:0.572274:0.000000:0.000000:0.000000
aA  bA:@0.824614:0.587148:0.876128:0.587148:0.876128:0.572274:0.824614:0.572274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ :@0.845052:0.587148:0.858705:0.587148:0.858705:0.572249:0.845052:0.572249:0.000000:0.000000
a A  B:@0.755242:0.605794:0.801814:0.605794:0.801814:0.590920:0.755242:0.590920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( +   ) = :@0.763669:0.605794:0.827244:0.605794:0.827244:0.590895:0.763669:0.590895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aA  aB:@0.827244:0.605794:0.877803:0.605794:0.877803:0.590920:0.827244:0.590920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ :@0.847682:0.605794:0.861335:0.605794:0.861335:0.590895:0.847682:0.590895:0.000000:0.000000
1  = :@0.755242:0.624440:0.789736:0.624440:0.789736:0.609541:0.755242:0.609541:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.763418:0.624440:0.772414:0.624440:0.772414:0.609566:0.763418:0.609566:0.000000
A:@0.789736:0.624440:0.798732:0.624440:0.798732:0.609566:0.789736:0.609566:0.000000
     Matemática:@0.776108:0.266148:0.883649:0.266148:0.883649:0.249247:0.776108:0.249247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000