Question

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

Answer 1

$(2\hat{i}+3\hat{j}+8\hat{k})$ and $(-4\hat{i}+4\hat{j}+\alpha \hat{k})$ are perpendicular.

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

$\Rightarrow \alpha =-\frac{1}{2}$