Unit vectors perpendiculars to the plane of vectors $\vec{a}=\hat{i}-\hat{j}-3 \hat{k}, \vec{b}=\hat{i}+3 \hat{j}-\hat{k}$ are:

$\pm\left[\frac{-5 \hat{i}+\hat{j}+2 \hat{k}}{\sqrt{30}}\right]$ $\pm\left[\frac{5 \hat{i}+\hat{j}-2 \hat{k}}{\sqrt{30}}\right]$ $\pm\left[\frac{5 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{30}}\right]$ $\pm\left[\frac{-5 \hat{i}-\hat{j}-2 \hat{k}}{\sqrt{30}}\right]$

$\pm\left[\frac{5 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{30}}\right]$

The correct answer is Option (3) - $\pm\left[\frac{5 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{30}}\right]$