question_answer

Let \[\vec{p}\] and \[\vec{q}\] be the position vectors of P and Q respectively, with respect to O and \[|\vec{p}|\,\,=p,\,|\vec{q}|\,=q\] The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If OR and OS are perpendicular, then

A)  \[9{{p}^{2}}=4\,{{q}^{2}}\] 

B)  \[4{{p}^{2}}=9{{q}^{2}}\]  

C)  \[9p=4q\]       

D)  \[4p=9q\]