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 POQ internally and externally in the ratio $2:3$ respectively. If OR and OS are perpendicular then

Question

$\begin{array}{1 1} 9p^2=4q^2 \\ 4p^2=9q^2 \\ 9p=4q \\ 4p=9q \end{array}$