Question

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

Answer 1

Let the given vector be $\overrightarrow{a}=x(\hat{i}+\hat{j}+\hat{k})$

then $\overrightarrow{a}=x\hat{i}+x\hat{j}+x\hat{k}$

$\overrightarrow{a}=\sqrt{x^2+x^2+x^2}=\sqrt{3}x$

Therefore $\overrightarrow{a}$ will be unit vector if $|\overrightarrow{a}|=1$

$|\overrightarrow{a}=1|$

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

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