Which is a unit vector perpendicular to both $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} - \hat{j}$?

Explanation

1. 01

   $\vec{a} \times \vec{b} = \hat{i} + \hat{j} - 2\hat{k}$ is perpendicular to both; its magnitude is $\sqrt{1 + 1 + 4} = \sqrt{6}$.

2. 02

   Dividing gives $\frac{1}{\sqrt{6}}(\hat{i} + \hat{j} - 2\hat{k})$; its negative works too.