The unit vector perpendicular to each of the vectors \(\rm \vec{a}+\vec{b}\) and \(\rm \vec{a}-\vec{b} \), where \(\rm \vec{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\rm \vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}\), is :
1
\( \frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{1}{\sqrt{6}} \hat{\mathrm{k}}\)
2
\( -\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{1}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}\)
3
\(-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{2}{\sqrt{6}} \hat{\mathrm{k}}\)
4
\(-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}\)