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:

Question

Aicharya · Accepted Answer

$\vec{a}=2 \hat{i}+3 \hat{i}+8 \hat{k}, b=4 \hat{j}+3 \hat{i}+\alpha \hat{k}$
$\begin{aligned}
& \vec{a} \cdot \vec{b}=0, \text { if } a^{-1} \cdot b^{-1} \\
& \therefore(2 \hat{i}+3 \hat{j}+8 \hat{k}) \cdot(-4 i+4 j+\alpha k)=\frac{1}{2} \\
& \Rightarrow \alpha=-\frac{1}{2}
\end{aligned}$

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

Solution