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 (…

Let the point A divide the line segment joining the points $\displaystyle \mathrm{P}(-1,-1,2)$ and $\displaystyle \mathrm{Q}(5,5,10)$ internally in the ratio $\displaystyle \mathrm{r}: 1(\mathrm{r}>0)$. If O is the origin and $\displaystyle (\overrightarrow{\mathrm{OQ}} \cdot \overrightarrow{\mathrm{OA}})-\frac{1}{5}|\overrightarrow{\mathrm{OP}} \times \overrightarrow{\mathrm{OA}}|^2=10$, then the value of r is :