JEE Advance - Mathematics (1994 - No. 11)
Let $$\overrightarrow p $$ and $$\overrightarrow q $$ be the position vectors of $$P$$ and $$Q$$ respectively, with respect to $$O$$ and $$\left| {\overrightarrow p } \right| = p,\left| {\overrightarrow q } \right| = q.$$ The points $$R$$ and $$S$$ divide $$PQ$$ internally and externally in the ratio $$2:3$$ respectively. If $$OR$$ and $$OS$$ are perpendicular then
$$9{q^2} = 4{q^2}$$
$$4{p^2} = 9{q^2}$$
$$9p = 4q$$
$$4p = 9q$$