140:@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
2.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 función :@0.154723:0.192000:0.247832:0.192000:0.247832:0.177101:0.154723:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométrica relaciona :@0.079672:0.207088:0.247831:0.207088:0.247831:0.192189:0.079672:0.192189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el cateto adyacente con la :@0.069553:0.222175:0.247831:0.222175:0.247831:0.207276:0.069553:0.207276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipotenusa de un :@0.126143:0.237263:0.247832:0.237263:0.247832:0.222364:0.126143:0.222364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulo rectángulo?:@0.100545:0.252350:0.244162:0.252350:0.244162:0.237451:0.100545:0.237451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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
nidad de conocimientos:@0.306727:0.415947:0.480398:0.415947:0.480398:0.400582:0.306727:0.400582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.416732:0.297460:0.416732:0.297460:0.399597:0.284892:0.399597:0.000000
Sean los vectores :@0.287490:0.449220:0.417993:0.449220:0.417993:0.432831:0.287490:0.432831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.419385:0.449275:0.429281:0.449275:0.429281:0.432914:0.419385:0.432914:0.000000
a a:@0.450639:0.449275:0.483514:0.449275:0.483514:0.432914:0.450639:0.432914:0.000000:0.000000:0.000000
B:@0.512574:0.449275:0.521419:0.449275:0.521419:0.432914:0.512574:0.432914:0.000000
bb:@0.543300:0.449275:0.575806:0.449275:0.575806:0.432914:0.543300:0.432914:0.000000:0.000000
:@0.419963:0.437976:0.333906:0.437976:0.333906:0.421919:0.419963:0.421919:0.000000
:@0.513576:0.437976:0.427519:0.437976:0.427519:0.421919:0.513576:0.421919:0.000000
=:@0.432420:0.449953:0.349607:0.449953:0.349607:0.434380:0.432420:0.434380:0.000000
=:@0.525351:0.449953:0.442537:0.449953:0.442537:0.434380:0.525351:0.434380:0.000000
(,:@0.445142:0.449275:0.467716:0.449275:0.467716:0.432886:0.445142:0.432886:0.000000:0.000000
):@0.490640:0.449275:0.495523:0.449275:0.495523:0.432886:0.490640:0.432886:0.000000
( , :@0.538073:0.449275:0.566557:0.449275:0.566557:0.432886:0.538073:0.432886:0.000000:0.000000:0.000000:0.000000
), se cumplen los siguientes teoremas.:@0.582569:0.449275:0.858780:0.449220:0.858780:0.432831:0.582569:0.432886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.458754:0.451279:0.463965:0.451279:0.463965:0.441781:0.458754:0.441781:0.000000
2:@0.483050:0.451279:0.488261:0.451279:0.488261:0.441781:0.483050:0.441781:0.000000
1:@0.551047:0.451279:0.556259:0.451279:0.556259:0.441781:0.551047:0.441781:0.000000
2:@0.574969:0.451279:0.580181:0.451279:0.580181:0.441781:0.574969:0.441781:0.000000
y :@0.499849:0.449275:0.511937:0.449275:0.511937:0.432886:0.499849:0.432886:0.000000:0.000000
Ley del paralelogramo:@0.287495:0.485536:0.513607:0.485536:0.513607:0.464026:0.287495:0.464026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ley del paralelogramo de vectores es un método geométrico utilizado para sumar :@0.287495:0.508317:0.907711:0.508317:0.907711:0.491928:0.287495:0.491928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos vectores que actúan sobre un mismo punto, como se puede apreciar :@0.287495:0.524913:0.828488:0.524913:0.828488:0.508524:0.287495:0.508524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para los vectores   y  , se cumple la siguiente igualdad::@0.287495:0.550928:0.699448:0.550930:0.699448:0.534542:0.287495:0.534539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.416653:0.551152:0.452624:0.551152:0.452624:0.534790:0.416653:0.534790:0.000000:0.000000
:@0.417224:0.539852:0.397249:0.539852:0.397249:0.523795:0.417224:0.523795:0.000000
:@0.444755:0.539852:0.424780:0.539852:0.424780:0.523795:0.444755:0.523795:0.000000
AB:@0.478461:0.581805:0.513370:0.581805:0.513370:0.565712:0.478461:0.565712:0.000000:0.000000
AB:@0.549550:0.581805:0.584458:0.581805:0.584458:0.565712:0.549550:0.565712:0.000000:0.000000
A:@0.638555:0.581805:0.648901:0.581805:0.648901:0.565712:0.638555:0.565712:0.000000
B:@0.682962:0.581805:0.692209:0.581805:0.692209:0.565712:0.682962:0.565712:0.000000
=2:@0.601469:0.581805:0.624992:0.581805:0.624992:0.565423:0.601469:0.565423:0.000000:0.000000
.:@0.714594:0.581805:0.717947:0.581805:0.717947:0.565423:0.714594:0.565423:0.000000
2:@0.521887:0.569154:0.527609:0.569154:0.527609:0.559182:0.521887:0.559182:0.000000
2:@0.597207:0.569154:0.602930:0.569154:0.602930:0.559182:0.597207:0.559182:0.000000
2:@0.657385:0.569046:0.662827:0.569046:0.662827:0.559564:0.657385:0.559564:0.000000
2:@0.701252:0.569046:0.706694:0.569046:0.706694:0.559564:0.701252:0.559564:0.000000
+:@0.491955:0.582513:0.464830:0.582513:0.464830:0.566232:0.491955:0.566232:0.000000
+:@0.529657:0.582513:0.502532:0.582513:0.502532:0.566232:0.529657:0.566232:0.000000
−:@0.563047:0.582513:0.471537:0.582513:0.471537:0.566232:0.563047:0.566232:0.000000
+:@0.665134:0.582513:0.573624:0.582513:0.573624:0.566232:0.665134:0.566232:0.000000
Teorema de Pitágoras:@0.287495:0.632801:0.506289:0.632801:0.506289:0.611291:0.287495:0.611291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.465161:0.661868:0.502127:0.661868:0.502127:0.645507:0.465161:0.645507:0.000000:0.000000
AB:@0.592220:0.661868:0.626200:0.661868:0.626200:0.645507:0.592220:0.645507:0.000000:0.000000
A:@0.662525:0.661868:0.672420:0.661868:0.672420:0.645507:0.662525:0.645507:0.000000
B:@0.705922:0.661868:0.714767:0.661868:0.714767:0.645507:0.705922:0.645507:0.000000
:@0.465736:0.650569:0.444765:0.650569:0.444765:0.634512:0.465736:0.634512:0.000000
:@0.494262:0.650569:0.473291:0.650569:0.473291:0.634512:0.494262:0.634512:0.000000
:@0.592794:0.650569:0.625890:0.650569:0.625890:0.634512:0.592794:0.634512:0.000000:0.000000
:@0.663096:0.650569:0.626830:0.650569:0.626830:0.634512:0.663096:0.634512:0.000000
:@0.706917:0.650569:0.670651:0.650569:0.670651:0.634512:0.706917:0.634512:0.000000
⊥:@0.478193:0.662546:0.490318:0.662546:0.490318:0.646973:0.478193:0.646973:0.000000
+:@0.604625:0.662546:0.614742:0.662546:0.614742:0.646973:0.604625:0.646973:0.000000
=:@0.642936:0.662546:0.653053:0.662546:0.653053:0.646973:0.642936:0.646973:0.000000
+:@0.687752:0.662546:0.697869:0.662546:0.697869:0.646973:0.687752:0.646973:0.000000
 si y solo si :@0.503377:0.661868:0.583261:0.661868:0.583261:0.645479:0.503377:0.645479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.632422:0.649491:0.637634:0.649491:0.637634:0.639993:0.632422:0.639993:0.000000
2:@0.677864:0.649491:0.683076:0.649491:0.683076:0.639993:0.677864:0.639993:0.000000
2:@0.720999:0.649491:0.726211:0.649491:0.726211:0.639993:0.720999:0.639993:0.000000
Ángulo entre dos vectores :@0.287495:0.711812:0.557605:0.711812:0.557605:0.690302:0.287495:0.690302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Del producto escalar :@0.287495:0.738478:0.444702:0.738478:0.444702:0.722089:0.287495:0.722089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.445809:0.738337:0.472253:0.738337:0.472253:0.722944:0.445809:0.722944:0.000000:0.000000
A:@0.495748:0.738337:0.505643:0.738337:0.505643:0.722944:0.495748:0.722944:0.000000
B Cos  θ:@0.525011:0.738337:0.582468:0.738337:0.582468:0.722944:0.525011:0.722944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.446380:0.727038:0.471939:0.727038:0.471939:0.710981:0.446380:0.710981:0.000000:0.000000
:@0.496319:0.727038:0.474187:0.727038:0.474187:0.710981:0.496319:0.710981:0.000000
:@0.526006:0.727038:0.503874:0.727038:0.503874:0.710981:0.526006:0.710981:0.000000
⋅=:@0.457326:0.739015:0.486294:0.739015:0.486294:0.723442:0.457326:0.723442:0.000000:0.000000
 :@0.513236:0.738337:0.517271:0.738337:0.517271:0.722668:0.513236:0.722668:0.000000
(   ):@0.567358:0.737176:0.589231:0.737176:0.589231:0.721506:0.567358:0.721506:0.000000:0.000000:0.000000:0.000000:0.000000
, se tiene que el ángulo entre dos vectores :@0.589233:0.738478:0.907718:0.738478:0.907718:0.722089:0.589233:0.722089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se puede calcular mediante la expresión:@0.287499:0.759846:0.582077:0.759846:0.582077:0.743457:0.287499:0.743457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.536439:0.796724:0.546556:0.796724:0.546556:0.781151:0.536439:0.781151:0.000000
⋅:@0.623178:0.787969:0.627785:0.787969:0.627785:0.772396:0.623178:0.772396:0.000000
⎛:@0.588792:0.781317:0.595869:0.781317:0.595869:0.765744:0.588792:0.765744:0.000000
⎝:@0.588792:0.816875:0.595869:0.816875:0.595869:0.801302:0.588792:0.801302:0.000000
⎜:@0.588792:0.793861:0.595869:0.793861:0.595869:0.778288:0.588792:0.778288:0.000000
⎜:@0.588792:0.807028:0.595869:0.807028:0.595869:0.791455:0.588792:0.791455:0.000000
⎞:@0.653344:0.781317:0.660421:0.781317:0.660421:0.765744:0.653344:0.765744:0.000000
⎠:@0.653344:0.816875:0.660421:0.816875:0.660421:0.801302:0.653344:0.801302:0.000000
⎟:@0.653344:0.793861:0.660421:0.793861:0.660421:0.778288:0.653344:0.778288:0.000000
⎟:@0.653344:0.807028:0.660421:0.807028:0.660421:0.791455:0.653344:0.791455:0.000000
−:@0.575808:0.788777:0.581671:0.788777:0.581671:0.779752:0.575808:0.779752:0.000000
Cos:@0.549474:0.796046:0.574849:0.796046:0.574849:0.780653:0.549474:0.780653:0.000000:0.000000:0.000000
AB:@0.611668:0.787292:0.638111:0.787292:0.638111:0.771899:0.611668:0.771899:0.000000:0.000000
A:@0.605863:0.808770:0.615759:0.808770:0.615759:0.793377:0.605863:0.793377:0.000000
B:@0.635126:0.808770:0.643971:0.808770:0.643971:0.793377:0.635126:0.793377:0.000000
1:@0.581606:0.788384:0.586817:0.788384:0.586817:0.779303:0.581606:0.779303:0.000000
:@0.612244:0.775991:0.637803:0.775991:0.637803:0.759934:0.612244:0.759934:0.000000:0.000000
:@0.606439:0.797497:0.584308:0.797497:0.584308:0.781440:0.606439:0.781440:0.000000
:@0.636126:0.797497:0.613995:0.797497:0.613995:0.781440:0.636126:0.781440:0.000000
 :@0.623356:0.808783:0.627392:0.808783:0.627392:0.793113:0.623356:0.793113:0.000000
θ:@0.525339:0.796197:0.534406:0.796197:0.534406:0.780804:0.525339:0.780804:0.000000
Ley de cosenos:@0.287495:0.853178:0.439848:0.853178:0.439848:0.831668:0.287495:0.831668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para los vectores   y   no nulos y con :@0.287495:0.878255:0.572710:0.878255:0.572710:0.861866:0.287495:0.861866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.416653:0.878475:0.452624:0.878475:0.452624:0.862114:0.416653:0.862114:0.000000:0.000000
:@0.417224:0.867176:0.397249:0.867176:0.397249:0.851119:0.417224:0.851119:0.000000
:@0.444755:0.867176:0.424780:0.867176:0.424780:0.851119:0.444755:0.851119:0.000000
θ Є:@0.572710:0.878255:0.594989:0.878255:0.594989:0.861894:0.572710:0.861894:0.000000:0.000000:0.000000
 [0,  ], se tiene::@0.594989:0.878255:0.701832:0.878255:0.701832:0.861866:0.594989:0.861866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.620143:0.878255:0.629357:0.878255:0.629357:0.861894:0.620143:0.861894:0.000000
BA:@0.468518:0.906684:0.504065:0.906684:0.504065:0.891291:0.468518:0.891291:0.000000:0.000000
B:@0.538507:0.906684:0.547352:0.906684:0.547352:0.891291:0.538507:0.891291:0.000000
A:@0.582751:0.906684:0.592647:0.906684:0.592647:0.891291:0.582751:0.891291:0.000000
AB Cos:@0.636984:0.906684:0.705701:0.906684:0.705701:0.891291:0.636984:0.891291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.480662:0.907361:0.451418:0.907361:0.451418:0.891789:0.480662:0.891789:0.000000
=:@0.520024:0.907361:0.490779:0.907361:0.490779:0.891789:0.520024:0.891789:0.000000
+:@0.563476:0.907361:0.529090:0.907361:0.529090:0.891789:0.563476:0.891789:0.000000
−:@0.607979:0.907361:0.573593:0.907361:0.573593:0.891789:0.607979:0.891789:0.000000
2:@0.509510:0.897127:0.514722:0.897127:0.514722:0.888045:0.509510:0.888045:0.000000
2:@0.553574:0.894297:0.558786:0.894297:0.558786:0.885216:0.553574:0.885216:0.000000
 :@0.539507:0.895381:0.502522:0.895381:0.502522:0.879324:0.539507:0.879324:0.000000:0.000000:0.000000
:@0.583328:0.895381:0.547062:0.895381:0.547062:0.879324:0.583328:0.879324:0.000000
:@0.469666:0.895381:0.477221:0.895381:0.477221:0.879324:0.469666:0.879324:0.000000
:@0.637542:0.895381:0.667616:0.895381:0.667616:0.879324:0.637542:0.879324:0.000000:0.000000
2:@0.598075:0.894298:0.603286:0.894298:0.603286:0.885216:0.598075:0.885216:0.000000
2:@0.620391:0.906684:0.629383:0.906684:0.629383:0.891014:0.620391:0.891014:0.000000
θ:@0.712529:0.906836:0.721595:0.906836:0.721595:0.891443:0.712529:0.891443:0.000000
(  ):@0.708383:0.905785:0.726221:0.905785:0.726221:0.890115:0.708383:0.890115:0.000000:0.000000:0.000000:0.000000
Pienso y progreso:@0.294883:0.347425:0.417347:0.347425:0.417347:0.332061:0.294883:0.332061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Investiga la aplicación de los vectores en la representación de fuerzas que actúan sobre :@0.294883:0.366077:0.879314:0.366077:0.879314:0.351178:0.294883:0.351178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un cuerpo.:@0.294883:0.381165:0.366749:0.381165:0.366749:0.366266:0.294883:0.366266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En aeronáutica, conocer la dirección relativa entre dos rutas de vuelo es fundamental :@0.287495:0.168345:0.907696:0.168345:0.907696:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para prevenir colisiones y planificar trayectorias eficientes. Para ello, se puede calcular :@0.287495:0.184941:0.907676:0.184941:0.907676:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el ángulo entre los vectores que representan la dirección de vuelo de cada avión.:@0.287495:0.201538:0.879938:0.201538:0.879938:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos aviones despegan desde un aeropuerto al mismo tiempo. El primer avión vuela :@0.287495:0.225257:0.907683:0.225257:0.907683:0.208868:0.287495:0.208868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguiendo una dirección representada por el vector   = (3, 4), y el segundo avión :@0.287495:0.241853:0.907679:0.241858:0.907679:0.225469:0.287495:0.225464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.678493:0.241853:0.686233:0.241853:0.686233:0.225492:0.678493:0.225492:0.000000
1:@0.686226:0.245022:0.691469:0.245022:0.691469:0.235467:0.686226:0.235467:0.000000
toma una ruta diferente representada por el vector   = (5, 0), ambos en el mismo :@0.287497:0.258455:0.907693:0.258455:0.907693:0.242066:0.287497:0.242066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.674588:0.258455:0.682328:0.258455:0.682328:0.242093:0.674588:0.242093:0.000000
2:@0.682324:0.261618:0.687567:0.261618:0.687567:0.252063:0.682324:0.252063:0.000000
plano horizontal.:@0.287502:0.275051:0.410689:0.275051:0.410689:0.258662:0.287502:0.258662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.287502:0.298770:0.302410:0.298770:0.302410:0.281869:0.287502:0.281869:0.000000:0.000000
  ¿Qué ángulo en grados forman las trayectorias de los dos aviones?:@0.302410:0.298770:0.801775:0.298770:0.801775:0.282381:0.302410:0.282381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.287502:0.318935:0.303718:0.318935:0.303718:0.302034:0.287502:0.302034:0.000000:0.000000
  ¿Cuál es la proyección ortogonal del vector   sobre el vector  ?:@0.303718:0.318935:0.785479:0.318936:0.785479:0.302547:0.303718:0.302546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.636112:0.318935:0.643852:0.318935:0.643852:0.302573:0.636112:0.302573:0.000000
1:@0.643847:0.322100:0.649090:0.322100:0.649090:0.312545:0.643847:0.312545:0.000000
v:@0.765476:0.318936:0.773216:0.318936:0.773216:0.302575:0.765476:0.302575:0.000000
2:@0.773216:0.322100:0.778459:0.322100:0.778459:0.312545:0.773216:0.312545:0.000000
Aplicaciones geométricas :@0.286308:0.060073:0.669455:0.060073:0.669455:0.026520:0.286308:0.026520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las operaciones con vectores:@0.286308:0.090250:0.752232:0.090250:0.752232:0.056698:0.286308:0.056698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.094760:0.108603:0.159692:0.108603:0.159692:0.011514:0.094760:0.011514:0.000000
©Shutterstock:@0.070380:0.376824:0.070380:0.333999:0.058469:0.333999:0.058469:0.376824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vectores permiten :@0.072616:0.434126:0.209032:0.434126:0.209032:0.420717:0.072616:0.420717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
planificar rutas, evitar :@0.072616:0.446698:0.202564:0.446698:0.202564:0.433289:0.072616:0.433289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
colisiones, ajustar el rumbo :@0.072616:0.459269:0.238493:0.459269:0.238493:0.445860:0.072616:0.445860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
según el viento y coordinar :@0.072616:0.471841:0.239217:0.471841:0.239217:0.458432:0.072616:0.458432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
movimientos entre aeronaves :@0.072616:0.484413:0.254475:0.484413:0.254475:0.471004:0.072616:0.471004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de forma precisa y segura.:@0.072616:0.496985:0.228783:0.496985:0.228783:0.483576:0.072616:0.483576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Método del paralelogramo :@0.072616:0.694820:0.237135:0.694820:0.237135:0.681411:0.072616:0.681411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para sumar y restar vectores:@0.072616:0.707391:0.240075:0.707391:0.240075:0.693982:0.072616:0.693982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A + B:@0.222726:0.559908:0.255778:0.559908:0.255778:0.545914:0.222726:0.545914:0.000000:0.000000:0.000000:0.000000:0.000000
A – B:@0.132422:0.648575:0.163866:0.648575:0.163866:0.634581:0.132422:0.634581:0.000000:0.000000:0.000000:0.000000:0.000000
A – B:@0.163814:0.578238:0.195258:0.578238:0.195258:0.564244:0.163814:0.564244:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.181201:0.562773:0.190197:0.562773:0.190197:0.548779:0.181201:0.548779:0.000000
B:@0.219325:0.596504:0.227366:0.596504:0.227366:0.582510:0.219325:0.582510:0.000000
–B:@0.193227:0.639323:0.209640:0.639611:0.210076:0.625621:0.193663:0.625333:0.000000:0.000000
–B:@0.087338:0.644649:0.103751:0.644936:0.104186:0.630947:0.087773:0.630659:0.000000:0.000000
B:@0.128584:0.581230:0.136625:0.581230:0.136625:0.567236:0.128584:0.567236:0.000000
A:@0.162089:0.607291:0.171085:0.607291:0.171085:0.593298:0.162089:0.593298:0.000000
0:@0.123642:0.621273:0.131382:0.621273:0.131382:0.607279:0.123642:0.607279:0.000000
x:@0.247307:0.619676:0.254092:0.619676:0.254092:0.605682:0.247307:0.605682:0.000000
y:@0.114288:0.549350:0.121090:0.549350:0.121090:0.535356:0.114288:0.535356:0.000000
A – B:@0.224215:0.904564:0.255659:0.904564:0.255659:0.890570:0.224215:0.890570:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.137453:0.899541:0.146449:0.899541:0.146449:0.885547:0.137453:0.885547:0.000000
B:@0.177786:0.841850:0.185827:0.841850:0.185827:0.827856:0.177786:0.827856:0.000000
θ:@0.101680:0.871975:0.109922:0.871975:0.109922:0.857981:0.101680:0.857981:0.000000