Let \( P \) be the foot of the perpendicular from the point \( (1, 2, 2) \) on the line \( L : \dfrac{x-1}{1}=\dfrac{y+1}{-1}=\dfrac{z-2}{2} \).
Let the line \( \vec{r}=(\hat{-i}+\hat{j}-2\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}),\, \lambda\in\mathbb{R} \), intersect the line \( L \) at \( Q \). Then \( 2(PQ)^2 \) is equal to:
