Question

For what values of c are the vectors [−8, 𝑐, 4] and [𝑐, 𝑐 2 , 𝑐] orthogonal?

Answer 1

Let $\vec c_1=-8\hat{i}+c\hat{j}+4\hat{k}, \vec c_2=c\hat{i}+c^2\hat{j}+c\hat{k}$

For vectors to be orthogonal, $\vec c_1.\vec c_2=0$

$\therefore-8c+c^3+4c=0\\ \Rightarrow c(c^2-4)=0\\ \Rightarrow c=0,2,-2$