Let \( \vec{p} \) and \( \vec{q} \) be the position vectors of \( \mathrm{P}^{2} \) and \( Q \) ...

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