The values of \(x\) for which \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector are

\(\pm \frac{1}{\sqrt{3}}\) \(\pm \frac{1}{\sqrt{2}}\) \(\pm 1\) \(\pm 2\)

\(\pm \frac{1}{\sqrt{3}}\)

\(\begin{aligned}\text{Given, }|x(\hat{i}+\hat{j}+\hat{k}|^{2}&=1\\ |x|^{2} 3&=1\\ |x|^{2}&=\frac{1}{3}\\ |x|&=\pm \frac{1}{\sqrt{3}}\end{aligned}\)