What is the area of the triangle with vertices $A(1, 0, 1)$, $B(2, 2, 3)$ and $C(0, 3, 1)$?

Explanation

1. 01

   $\overrightarrow{AB} = \hat{i} + 2\hat{j} + 2\hat{k}$, $\overrightarrow{AC} = -\hat{i} + 3\hat{j}$, and $\overrightarrow{AB} \times \overrightarrow{AC} = -6\hat{i} - 2\hat{j} + 5\hat{k}$.

2. 02

   Area $= \frac{1}{2}\sqrt{36 + 4 + 25} = \frac{\sqrt{65}}{2}$.