Question

If $\overline{p}=-\overline{i}+3\overline{j}+a\overline{k}$ is perpendicular to $\overline{q}=4\overline{i}+2\overline{j}+\overline{k}$ then the value of $a$ is

• A. $2$
• B. $-2$
• C. $0$
• D. $-1$

Answer 1

Answer: (B)

$-2$

$\overrightarrow{P}\perp \overrightarrow{Q}$

$\therefore \overrightarrow{P}\cdot \overrightarrow{Q}=0$

$\therefore (-1)\left(4\right)+\left(3\right)\left(2\right)+\left(a\right)\left(1\right)=0$

$\Rightarrow a=-2$