Triangle Trigonometry and Vectors · Superchallenge problem

Point $P$ lies inside $\triangle ABC$ and satisfies $\overrightarrow{PA}+2\,\overrightarrow{PB}+3\,\overrightarrow{PC}=\mathbf{0}$. The area of $\triangle ABC$ is $30$. Find the area of $\triangle PBC$.