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

Explanation

1. 01

   $\vec{a} \times \vec{b}$ is perpendicular to both.

2. 02

   $\hat{i}(1 - 0) - \hat{j}(1 - 0) + \hat{k}(1 - 0) = \hat{i} - \hat{j} + \hat{k}$; its dot product with each is 0.