Let $p$ and $q$ be the position vectors of $P$ and $Q$ respectively with respect to $O$ and $|p| = p, |q| = q.$ The points $R$ and $S$ divide $PQ$ internally and externally in the ratio $2 : 3$ respectively. If $\overrightarrow{OR}$ and $\overrightarrow{OS}$ are perpendicular,then:
- A$9p^2 = 4q^2$
- B$4p^2 = 9q^2$
- C$9p = 4q$
- D$4p = 9q$
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