Trigonometry · Superchallenge problem

In $\triangle ABC$, $\overrightarrow{AB}\cdot\overrightarrow{AC} = 3$, $\;\overrightarrow{BA}\cdot\overrightarrow{BC} = 5$, and $\overrightarrow{CA}\cdot\overrightarrow{CB} = 2$. Find the area of the triangle.