Question

Dados os pontos A(4,0,-1), B(2,-2,1) e C(1,2,2) e os vetores u= (2,1,1) e v= (-1,-2,3), obter o vetor x tal que (BC . v)x= (u . v)v - 3x.

Answer 1

(B.C.v)+x =(u.v).v-3x

[(2,-2,1).(1,2,2).(-1,-2,3)]+x=[(2,1,1).(-1,-2,3)].(-1,-2,3)-3x

[(2,-4,2).(-1,-2,3)]+x=[(-2,-2,3)].(-1,-2,3)-3x

[(-2,8,6)]+x+3x=(2,4,9)

4x=(2,4,9)-(-2,8,6)

4x= (4,-4,3)

x=(1,-1,3/4)