Question

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

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

Answer 1

The correct option is B

$-\frac{1}{2}$

Vectors are perpendicular to each other
Cross product is zero
$\overrightarrow{A}=2\hat{i}+3\hat{j}+8\hat{k}\overrightarrow{B}=4\hat{j}-4\hat{i}+\alpha \hat{k}\overrightarrow{A}.\overrightarrow{B}=0-8+12+8\alpha =08\alpha =-4\alpha =-\frac{1}{2}$