Question

calcular a e b de modo que sejam colineares os pontos A(3, 1, -2), B(1, 5, 1) e C(a, b, 7).

Answer 1

vetor AB = B-A =(1, 5, 1)-(3, 1, -2)=(-2,4,3)
vetor BC = C-B =(a, b, 7)-(1, 5, 1)=(a-1,b-5,6)

-2/(a-1)=4/(b-5)=3/6
-2/(a-1)=3/6
3a-3 =-12
a=-3
4/(b-5)=3/6
3b-15=24
b=13