Dados os pontos A (- 1,3) , B (2 , 5) e C (3 , - 1) , calcular vec O A - vec A B , vec O C - vec B C e 3 vec B A - 4 vec C B

Passo 1

Primeiro, vamos calcular os vetores vec O A , vec O C , vec A B , vec B C , vec B A e vec C B

Para calcular vetores usando os pontos, temos que fazer:

(c o o r d e n a d a d o v e t o r) = (c o o r d e n a d a a e x t r e m i d a d e - c o o r d e n a d a d a o r i g e m)

Se adotarmos vec O = ( 0 , 0 ) temos:

[[vec O A,=,(- 1,3),-,(0 , 0)],[vec O C,=,(3 , - 1),-,(0 , 0)],[[[vec A B,=,(2 , 5),-,(- 1,3)],[vec B C,=,(3 , - 1),-,(2 , 5)],[[[vec B A,=,(- 1,3),-,(2 , 5)],[vec C B,=,(2 , 5),-,(3 , - 1)]]]]]]

[[vec O A,=,([[-,1,-,0,,,3,-,0]])],[vec O C,=,([[3,-,0,,,-,1,-,0]])],[[[vec A B,=,([[2,-,(- 1),,,5,-,3]])],[vec B C,=,([[3,-,2,,,-,1,-,5]])],[[[vec B A,=,([[-,1,-,2,,,3,-,5]])],[vec C B,=,([[2,-,3,,,5,-,(,-,1,)]])]]]]]]

[[vec O A,=,([[-,1,,,3]])],[vec O C,=,([[3,,,-,1]])],[[[vec A B,=,([[3,,,2]])],[vec B C,=,([[1,,,-,6]])],[[[vec B A,=,([[-,3,,,-,2]])],[vec C B,=,([[-,1,,,6]])]]]]]]

Passo 2

Agora, vamos calcular vec O A - vec A B , vec O C - vec B C e 3 vec B A - 4 vec C B usando os vetores que encontramos no Passo 1

[[vec O A,-,vec A B,=,([[-,1,,,3]]),-,([[3,,,2]])],[vec O C,-,vec B C,=,([[3,,,-,1]]),-,([[1,,,-,6]])],[3,vec B A,-,4,vec C B,=,3,([[-,3,,,-,2]]),-,4,([[-,1,,,6]])]]

[[vec O A,-,vec A B,=,([[-,1,,,3]]),-,([[3,,,2]])],[vec O C,-,vec B C,=,([[3,,,-,1]]),-,([[1,,,-,6]])],[3,vec B A,-,4,vec C B,=,([[-,9,,,-,6]]),-,([[-,4,,,24]])]]

[[vec O A,-,vec A B,=,([[-,1,-,3,,,3,-,2]])],[vec O C,-,vec B C,=,([[3,-,1,,,-,1,-,(,-,6,)]])],[3,vec B A,-,4,vec C B,=,([[-,9,-,(- 4),,,-,6,-,24]])]]

[[vec O A,-,vec A B,=,([[-,4,,,1]])],[vec O C,-,vec B C,=,([[2,,,5]])],[3,vec B A,-,4,vec C B,=,([[-,5,,,-,30]])]]

Resposta

[[vec O A,-,vec A B,=,([[-,4,,,1]])],[vec O C,-,vec B C,=,([[2,,,5]])],[3,vec B A,-,4,vec C B,=,([[-,5,,,-,30]])]]

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