Find the value of

$x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector if $|x(\hat{i}+\hat{j}+\hat{k})|=1$

Now,

$|x(\hat{i}+\hat{j}+\hat{k})|=1$

$\Rightarrow \sqrt{x^{2}+x^{2}+x^{2}}=1$

$\Rightarrow \sqrt{3 x^{2}}=1$

$\Rightarrow \sqrt{3} x=1$

$\Rightarrow x=\pm \frac{1}{\sqrt{3}}$

Hence, the required value of $x$ is $\pm \frac{1}{\sqrt{3}}$.