Question

For what value of $p$ , is $(\hat{i}+\hat{j}+\hat{k})$ p a unit vector?

Answer 1

Let $\overrightarrow{a}=p(\hat{i}+\hat{j}+\hat{k})$
Magnitude of $\overrightarrow{a}is|\overrightarrow{a}|$
$|\overrightarrow{a}|=\sqrt{(p{)}^2+(p{)}^2+(p{)}^2}=\pm \sqrt{3}p$
As $\overrightarrow{a}$ is a unit vector $|\overrightarrow{a}|=1$
$\therefore \Rightarrow \pm \sqrt{3p}=1\Rightarrow p=\pm \frac{1}{\sqrt{3}}$