What is the area of the triangle with vertices $A(1, 0, 2)$, $B(3, 1, 0)$ and $C(2, 4, 1)$?

Explanation

1. 01

   $\overrightarrow{AB} = 2\hat{i} + \hat{j} - 2\hat{k}$, $\overrightarrow{AC} = \hat{i} + 4\hat{j} - \hat{k}$, and $\overrightarrow{AB} \times \overrightarrow{AC} = 7\hat{i} + 7\hat{k}$.

2. 02

   Area $= \frac{1}{2}\sqrt{49 + 49} = \frac{7\sqrt{2}}{2}$.