The distance of the point Q (0,2,-2) form the line passing through the point P (5,-4, 3) and perpendicular to the lines r =(-3 i +2 k )+λ(2 i +3 j +5…

The distance of the point $\displaystyle \mathrm{Q}(0,2,-2)$ form the line passing through the point $\displaystyle \mathrm{P}(5,-4$, $\displaystyle 3$) and perpendicular to the lines $\displaystyle \vec{r}=(-3 \hat{i}+2 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+5 \hat{k}), \lambda \in \mathbb{R}$ and $\displaystyle \vec{r}=(\hat{i}-2 \hat{j}+\hat{k})+\mu(-\hat{i}+3 \hat{j}+2 \hat{k}), \mu \in \mathbb{R}$ is :