Vector Algebra

The unit vector perpendicular to each of the vectors \(\bar{a}+\bar{b}\) and \(\bar{a}-\bar{b}\), where \(\bar{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\overline{\mathrm{b}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) is