In triangle $ABC,$ points $P$ and $Q$ are on side $\overline{AB},$ and point $R$ is on side $\overline{AC}.$ If $AP = \frac{PQ}{3} = \frac{QB}{2}$ and $\frac{AR}{2} = \frac{RC}{3},$ then find $\frac{[QBC]}{[CRQ]}.$