:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
¿Qué es una magnitud?:@0.086308:0.192000:0.244164:0.192000:0.244164:0.177101:0.086308:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definiciones básicas:@0.287495:0.318242:0.492079:0.318242:0.492079:0.296732:0.287495:0.296732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recordemos que una cantidad o magnitud es todo aquello que se puede medir.:@0.287495:0.341023:0.875589:0.341023:0.875589:0.324634:0.287495:0.324634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Magnitudes escalares::@0.287495:0.364742:0.464954:0.364742:0.464954:0.347841:0.287495:0.347841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 son aquellas que quedan completamente definidas al co-:@0.464954:0.364742:0.903653:0.364742:0.903653:0.348353:0.464954:0.348353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nocer el número o módulo y la unidad de medida. Ejemplos: el tiempo, el dinero, :@0.287495:0.381338:0.907585:0.381338:0.907585:0.364949:0.287495:0.364949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la temperatura, etc.:@0.287495:0.397935:0.428594:0.397935:0.428594:0.381546:0.287495:0.381546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nidad de conocimientos:@0.306727:0.287113:0.480398:0.287113:0.480398:0.271749:0.306727:0.271749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.287899:0.297460:0.287899:0.297460:0.270764:0.284892:0.270764:0.000000
Pienso y progreso:@0.294883:0.231790:0.417347:0.231790:0.417347:0.216426:0.294883:0.216426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Por qué es importante guiarse con vectores en la navegación marítima?:@0.294883:0.250442:0.778300:0.250442:0.778300:0.235543:0.294883:0.235543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un barco parte desde el puerto P y se dirige al faro F, que se encuentra 6 km al este :@0.287495:0.168345:0.907655:0.168345:0.907655:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y 8 km al norte del puerto. ¿Cuál es la distancia directa entre el puerto y el faro? :@0.287495:0.184941:0.907560:0.184941:0.907560:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Representa el desplazamiento del barco mediante un vector.:@0.287495:0.201538:0.731981:0.201538:0.731981:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108603:0.159692:0.108603:0.159692:0.011514:0.094760:0.011514:0.000000
Vectores en :@0.286308:0.078354:0.466051:0.078354:0.466051:0.044801:0.286308:0.044801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.466051:0.079515:0.492660:0.079515:0.492660:0.044304:0.466051:0.044304:0.000000
2:@0.492655:0.066259:0.503356:0.066259:0.503356:0.046698:0.492655:0.046698:0.000000
. Deniciones:@0.503355:0.078354:0.701673:0.078354:0.701673:0.044801:0.503355:0.044801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.569105:0.078354:0.576181:0.078354:0.576181:0.044801:0.569105:0.044801:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.068421:0.285865:0.068421:0.243040:0.056510:0.243040:0.056510:0.285865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vectores se utilizan en la :@0.087907:0.374712:0.253997:0.374712:0.253997:0.361303:0.087907:0.361303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
navegación marítima.:@0.124997:0.387284:0.250695:0.387284:0.250695:0.373875:0.124997:0.373875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.789087:0.432220:0.798887:0.432220:0.798887:0.417321:0.789087:0.417321:0.000000
B:@0.893472:0.432220:0.901931:0.432220:0.901931:0.417321:0.893472:0.417321:0.000000
AB:@0.836312:0.426147:0.854572:0.426147:0.854572:0.411248:0.836312:0.411248:0.000000:0.000000
Magnitudes vectoriales::@0.287495:0.422057:0.479788:0.422057:0.479788:0.405156:0.287495:0.405156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 son aquellas que se representan me-:@0.479788:0.422057:0.768272:0.422057:0.768272:0.405668:0.479788:0.405668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diante su módulo, dirección y sentido que estén plenamente defi-:@0.287495:0.438653:0.768346:0.438653:0.768346:0.422265:0.287495:0.422265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nidos. Por ejemplo, la fuerza.:@0.287495:0.455250:0.495190:0.455250:0.495190:0.438861:0.287495:0.438861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición de vector::@0.287495:0.478900:0.454192:0.478900:0.454192:0.461999:0.287495:0.461999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 es un segmento de recta dirigido, que consta de magnitud, :@0.454192:0.478900:0.907694:0.478900:0.907694:0.462511:0.454192:0.462511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dirección y sentido.:@0.287495:0.495496:0.429626:0.495496:0.429626:0.479107:0.287495:0.479107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El módulo o magnitud es la longitud del vector. La dirección es el ángulo positivo que :@0.287495:0.519215:0.907585:0.519215:0.907585:0.502826:0.287495:0.502826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forma el vector con la horizontal en sentido antihorario. El sentido es la flecha que in-:@0.287495:0.535811:0.903552:0.535811:0.903552:0.519422:0.287495:0.519422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dica hacia dónde se dirige la recta.:@0.287495:0.552408:0.536488:0.552408:0.536488:0.536019:0.287495:0.536019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Igualdad de vectores:@0.287495:0.577964:0.468741:0.577964:0.468741:0.559527:0.287495:0.559527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos vectores son iguales si tienen la misma magnitud y la misma dirección.:@0.287495:0.601375:0.837811:0.601375:0.837811:0.584986:0.287495:0.584986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Magnitud o norma de un vector:@0.287495:0.634049:0.562137:0.634049:0.562137:0.615612:0.287495:0.615612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La magnitud, longitud o norma de un vector es la distancia que hay entre el punto :@0.287495:0.657460:0.907657:0.657460:0.907657:0.641071:0.287495:0.641071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inicial y el punto final.:@0.287495:0.674057:0.445566:0.674057:0.445566:0.657668:0.287495:0.657668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si el vector está en posición estándar, la :@0.287495:0.693640:0.587733:0.693640:0.587733:0.677251:0.287495:0.677251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
magnitud se calcula utilizando el Teore-:@0.287495:0.710237:0.583699:0.710237:0.583699:0.693848:0.287495:0.693848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ma de Pitágoras así: :@0.287495:0.726833:0.435635:0.726833:0.435635:0.710444:0.287495:0.710444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   ( ,  ) ó   = :@0.287495:0.750552:0.410795:0.750552:0.410795:0.734163:0.287495:0.734163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v a b:@0.317477:0.750552:0.360561:0.750552:0.360561:0.734191:0.317477:0.734191:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.318749:0.751091:0.325917:0.751091:0.325917:0.735961:0.318749:0.735961:0.000000
v:@0.383301:0.750552:0.391040:0.750552:0.391040:0.734191:0.383301:0.734191:0.000000
:@0.384572:0.751091:0.391741:0.751091:0.391741:0.735961:0.384572:0.735961:0.000000
a i:@0.410795:0.750552:0.427177:0.750552:0.427177:0.734191:0.410795:0.734191:0.000000:0.000000:0.000000
:@0.423031:0.749211:0.430199:0.749211:0.430199:0.734080:0.423031:0.734080:0.000000
 + :@0.430199:0.750552:0.449253:0.750552:0.449253:0.734163:0.430199:0.734163:0.000000:0.000000:0.000000
b j:@0.449253:0.750552:0.465470:0.750552:0.465470:0.734191:0.449253:0.734191:0.000000:0.000000:0.000000
:@0.460402:0.749211:0.467570:0.749211:0.467570:0.734080:0.460402:0.734080:0.000000
La magnitud o norma es: ||   || = :@0.287495:0.782307:0.521619:0.782307:0.521619:0.765918:0.287495:0.765918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.483197:0.782307:0.490937:0.782307:0.490937:0.765945:0.483197:0.765945:0.000000
:@0.484468:0.782846:0.491637:0.782846:0.491637:0.767716:0.484468:0.767716:0.000000
a:@0.531109:0.780384:0.540378:0.780384:0.540378:0.764023:0.531109:0.764023:0.000000
2:@0.540380:0.774329:0.545622:0.774329:0.545622:0.764774:0.540380:0.764774:0.000000
 + :@0.545623:0.780377:0.564677:0.780377:0.564677:0.763988:0.545623:0.763988:0.000000:0.000000:0.000000
b:@0.564677:0.780377:0.573946:0.780377:0.573946:0.764015:0.564677:0.764015:0.000000
2:@0.573945:0.774329:0.579187:0.774329:0.579187:0.764774:0.573945:0.764774:0.000000
En caso de que el vector sea libre, es de-:@0.607439:0.693634:0.903590:0.693634:0.903590:0.677245:0.607439:0.677245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cir definido por un punto inicial ( ,  ) y :@0.607439:0.710230:0.907676:0.710230:0.907676:0.693842:0.607439:0.693842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.852324:0.710230:0.880560:0.710230:0.880560:0.693869:0.852324:0.693869:0.000000:0.000000:0.000000
1:@0.859784:0.713394:0.865027:0.713394:0.865027:0.703839:0.859784:0.703839:0.000000
1:@0.880560:0.713394:0.885803:0.713394:0.885803:0.703839:0.880560:0.703839:0.000000
el punto final ( ,  ), la magnitud se cal-:@0.607434:0.726827:0.903615:0.726827:0.903615:0.710438:0.607434:0.710438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.715899:0.726827:0.744183:0.726827:0.744183:0.710466:0.715899:0.710466:0.000000:0.000000:0.000000
2:@0.723386:0.729990:0.728629:0.729990:0.728629:0.720436:0.723386:0.720436:0.000000
2:@0.744189:0.729990:0.749432:0.729990:0.749432:0.720436:0.744189:0.720436:0.000000
cula como la distancia entre dos puntos.:@0.607446:0.743423:0.902727:0.743423:0.902727:0.727034:0.607446:0.727034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
||   || =  (  –  )  + (  –  ):@0.607446:0.778303:0.781284:0.776632:0.781284:0.760243:0.607446:0.761914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.617268:0.778303:0.625008:0.778303:0.625008:0.761942:0.617268:0.761942:0.000000
:@0.618540:0.778843:0.625708:0.778843:0.625708:0.763712:0.618540:0.763712:0.000000
x:@0.667981:0.776630:0.675444:0.776630:0.675444:0.760269:0.667981:0.760269:0.000000
2:@0.675427:0.779796:0.680670:0.779796:0.680670:0.770241:0.675427:0.770241:0.000000
x:@0.693902:0.776632:0.701365:0.776632:0.701365:0.760271:0.693902:0.760271:0.000000
1:@0.701365:0.779796:0.706608:0.779796:0.706608:0.770241:0.701365:0.770241:0.000000
2:@0.711490:0.770585:0.716733:0.770585:0.716733:0.761030:0.711490:0.761030:0.000000
y:@0.737723:0.776632:0.745204:0.776632:0.745204:0.760271:0.737723:0.760271:0.000000
2:@0.745203:0.779796:0.750445:0.779796:0.750445:0.770241:0.745203:0.770241:0.000000
y:@0.763677:0.776632:0.771159:0.776632:0.771159:0.760271:0.763677:0.760271:0.000000
1:@0.771157:0.779796:0.776400:0.779796:0.776400:0.770241:0.771157:0.770241:0.000000
2:@0.781284:0.770585:0.786527:0.770585:0.786527:0.761030:0.781284:0.761030:0.000000
A:@0.674477:0.854517:0.681674:0.854517:0.681674:0.842618:0.674477:0.842618:0.000000
B:@0.759446:0.829371:0.765879:0.829371:0.765879:0.817472:0.759446:0.817472:0.000000
y:@0.647808:0.849770:0.653249:0.849770:0.653249:0.837870:0.647808:0.837870:0.000000
1:@0.653247:0.852065:0.657060:0.852065:0.657060:0.845116:0.653247:0.845116:0.000000
x:@0.684805:0.894245:0.690233:0.894245:0.690233:0.882346:0.684805:0.882346:0.000000
1:@0.690233:0.896546:0.694046:0.896546:0.694046:0.889597:0.690233:0.889597:0.000000
x:@0.757501:0.894245:0.762928:0.894245:0.762928:0.882346:0.757501:0.882346:0.000000
2:@0.762928:0.896546:0.766741:0.896546:0.766741:0.889597:0.762928:0.889597:0.000000
y:@0.648756:0.832162:0.654197:0.832162:0.654197:0.820263:0.648756:0.820263:0.000000
2:@0.654197:0.834463:0.658010:0.834463:0.658010:0.827514:0.654197:0.827514:0.000000
y:@0.776469:0.841867:0.781911:0.841867:0.781911:0.829968:0.776469:0.829968:0.000000
2:@0.781911:0.844168:0.785723:0.844168:0.785723:0.837219:0.781911:0.837219:0.000000
– :@0.785723:0.841867:0.795359:0.841867:0.795359:0.829948:0.785723:0.829948:0.000000:0.000000
y:@0.795359:0.841867:0.800801:0.841867:0.800801:0.829968:0.795359:0.829968:0.000000
1:@0.800801:0.844168:0.804613:0.844168:0.804613:0.837219:0.800801:0.837219:0.000000
x  x:@0.716065:0.866694:0.739847:0.866694:0.739847:0.854795:0.716065:0.854795:0.000000:0.000000:0.000000:0.000000
2:@0.721493:0.868995:0.725306:0.868995:0.725306:0.862046:0.721493:0.862046:0.000000
–:@0.725306:0.866694:0.732007:0.866694:0.732007:0.854775:0.725306:0.854775:0.000000
1:@0.739847:0.868995:0.743660:0.868995:0.743660:0.862046:0.739847:0.862046:0.000000
v:@0.719541:0.831350:0.725170:0.831350:0.725170:0.819451:0.719541:0.819451:0.000000
:@0.721150:0.831742:0.726363:0.831742:0.726363:0.820738:0.721150:0.820738:0.000000
y:@0.652103:0.812460:0.657544:0.812460:0.657544:0.800561:0.652103:0.800561:0.000000
x:@0.803357:0.892827:0.808785:0.892827:0.808785:0.880928:0.803357:0.880928:0.000000
A:@0.483761:0.845432:0.490958:0.845432:0.490958:0.833533:0.483761:0.833533:0.000000
a:@0.431266:0.896720:0.438007:0.896720:0.438007:0.884821:0.431266:0.884821:0.000000
b:@0.496493:0.867590:0.503234:0.867590:0.503234:0.855691:0.496493:0.855691:0.000000
y:@0.374536:0.817278:0.379977:0.817278:0.379977:0.805379:0.374536:0.805379:0.000000
x:@0.494188:0.892475:0.499616:0.892475:0.499616:0.880576:0.494188:0.880576:0.000000
v:@0.430107:0.858796:0.435736:0.858796:0.435736:0.846897:0.430107:0.846897:0.000000
:@0.431715:0.859188:0.436928:0.859188:0.436928:0.848184:0.431715:0.848184:0.000000
Los vectores están :@0.120769:0.473547:0.246646:0.473547:0.246646:0.458648:0.120769:0.458648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presentes en muchas :@0.100683:0.488635:0.246645:0.488635:0.246645:0.473736:0.100683:0.473736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
actividades de nuestra :@0.093211:0.503723:0.246646:0.503723:0.246646:0.488824:0.093211:0.488824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vida y nos ayudan :@0.123198:0.518810:0.246645:0.518810:0.246645:0.503911:0.123198:0.503911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a orientarnos:@0.155145:0.533898:0.242976:0.533898:0.242976:0.518999:0.155145:0.518999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de mejor manera, :@0.125225:0.548985:0.246646:0.548985:0.246646:0.534086:0.125225:0.534086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es común encontrar :@0.108154:0.564073:0.246646:0.564073:0.246646:0.549174:0.108154:0.549174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores en señales :@0.113297:0.579161:0.246646:0.579161:0.246646:0.564262:0.113297:0.564262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como las siguientes::@0.108489:0.594248:0.242976:0.594248:0.242976:0.579349:0.108489:0.579349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿En qué otras señales :@0.109779:0.877883:0.245991:0.877883:0.245991:0.863009:0.109779:0.863009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encuentras vectores?:@0.111840:0.892970:0.242976:0.892970:0.242976:0.878096:0.111840:0.878096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Seguridad vial:@0.128944:0.440928:0.237500:0.440928:0.237500:0.424027:0.128944:0.424027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.068421:0.681822:0.068421:0.638996:0.056510:0.638996:0.056510:0.681822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.2.1. :@0.298180:0.932779:0.346239:0.932779:0.346239:0.920488:0.298180:0.920488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Gracar vectores en el plano (coordenadas) identicando sus características: dirección, sentido y longitud :@0.346065:0.932779:0.906519:0.932779:0.906519:0.920860:0.346065:0.920860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.367709:0.932779:0.370644:0.932779:0.370644:0.920860:0.367709:0.920860:0.000000
 :@0.612682:0.932779:0.615617:0.932779:0.615617:0.920860:0.612682:0.920860:0.000000
o norma.:@0.298180:0.944095:0.345998:0.944095:0.345998:0.932176:0.298180:0.932176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.2.2. :@0.298180:0.955410:0.346239:0.955410:0.346239:0.943119:0.298180:0.943119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calcular la longitud o norma (aplicando el teorema de Pitágoras), para establecer la igualdad entre dos :@0.346992:0.955410:0.906578:0.955410:0.906578:0.943491:0.346992:0.943491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores.:@0.298180:0.966726:0.345449:0.966726:0.345449:0.954807:0.298180:0.954807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000