Question

If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{i}-4\hat{j}+\alpha \hat{k}$, then the value of $\alpha$ is

Answer 1

Dot product of two perpendicular vectors is zero.

So, $(2\hat{i}+3\hat{j}+8\hat{k}).(4\hat{i}-4\hat{j}+\alpha \hat{k})=0$

Or $8-12+8\alpha =0$

$⟹\alpha =0.5$