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

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

Answer 1

The correct option is A $\frac{1}{2}$

Given that the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are perpendicular meaning that $\overrightarrow{A}\cdot \overrightarrow{B}$$=0$.
$(2\hat{i}+3\hat{j}+8\hat{k})\cdot (4\hat{i}-4\hat{j}+\alpha \hat{k})=0$
$8-12+8\alpha =0$
$8\alpha =4$ or $\alpha =\frac{1}{2}$