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Question Id : 14602 | Context : JEE Main 2025 (23 January Evening Shift)
Let the point $A$ divide the line segment joining the points $P(-1,-1,2)$ and $Q(5,5,10)$ internally in the ratio $r:1\ (r>0)$. If $O$ is the origin and $(\overrightarrow{OQ}\cdot\overrightarrow{OA})-\dfrac{1}{5}\lvert\overrightarrow{OP}\times\overrightarrow{OA}\rvert^{2}=10$, then the value of $r$ is:


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