Vector Algebra: JEE Main 2025 Mathematics question

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 $(\overrightarrow{OQ} \cdot \overrightarrow{OA} - \frac{1}{5}|\overrightarrow{OP} \times \overrightarrow{OA}|^2 = 10)$, then the value of $r$ is: