If a vector $2 \hat{i}+3 \hat{j}+8 \hat{k}$ is perpendicular to the vector $4 \hat{j}-4 \hat{i}+\alp

Question

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

Professor PC Thomas Classes · Answer

(b) : $\vec{a}=2 \hat{i}+3 \hat{j}+8 \hat{k}, \vec{b}=4 \hat{j}-4 \hat{i}+\alpha \hat{k}$\ $\vec{a} \cdot \vec{b}=0$ if $\vec{a} \perp \vec{b}$\ $(2 \hat{i}+3 \hat{j}+8 \hat{k}) \cdot(-4 \hat{i}+4 \hat{j}+\alpha \hat{k})=0$\ or, $-8+12+8 \alpha=0 \Rightarrow 4+8 \alpha=0$\ $\Rightarrow \quad \alpha=-1 / 2$.\