Question

The vector $\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and $\overrightarrow{Q}=a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other. The positive value of $a$ is

Answer 1

Given,
$\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}$
$\overrightarrow{Q}=a\hat{i}-2\hat{j}-\hat{k}$
If two vectors are perpendicular, then their dot product must be zero.
$\overline{P}.\overline{Q}=0$
$\therefore a^2-2a-3=0$
$\Rightarrow a=3$
Final Answer: $\left(3\right)$