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 value of $\alpha$ is:

• A. $-1$
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. $1$

Answer 1

Answer: (B)

$\frac{1}{2}$

For perpendicular vectors.
$\overrightarrow{A}\cdot \overrightarrow{B}=0$
$(2\hat{i}+3\hat{j}+8\hat{k})\cdot (4\hat{i}-4\hat{j}+\alpha \hat{k})=0$
$8-12+8\alpha =0$
$-4+8\alpha =0$
$\Rightarrow \alpha =\frac{1}{2}$