What is the area of the parallelogram with adjacent sides $\hat{i} + 2\hat{j}$ and $\hat{j} + 3\hat{k}$?

Explanation

1. 01

   $\vec{a} \times \vec{b} = 6\hat{i} - 3\hat{j} + \hat{k}$.

2. 02

   Area $= \lvert \vec{a} \times \vec{b} \rvert = \sqrt{36 + 9 + 1} = \sqrt{46}$.