Let P be the foot of the perpendicular from the point (1,2,2) on the line L: (x-1)/1=(y+1)/-1=(z-2)/2. Let the line r =(- i + j -2 k )+λ( i - j + k…

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