Question

Find the value of x for which $x\left(\hat{i}+\hat{j}+\hat{k}\right)$ is a unit vector.

Answer 1

We have, $x\left(\hat{i}+\hat{j}+\hat{k}\right)$ is a unit vector.
$$\begin{gathered} \therefore \sqrt{x^2+x^2+x^2}=1 \\ \Rightarrow \sqrt{3}\left|x\right|=1 \\ \Rightarrow \left|x\right|=\frac{1}{\sqrt{3}} \\ \Rightarrow x=\pm \frac{1}{\sqrt{3}} \end{gathered}$$