area of triangle given three vertices

Problem

Given three vertices of the triangle $P$, $Q$, and $R$, calculate the vectors $\overrightarrow{PQ}$ and $\overrightarrow{PR}$.

Solution

The area of the parallelogram is $\overrightarrow{PQ}\times \overrightarrow{PR}$, their cross product. The corresponding triangle is half the area.