Vector Algebra: JEE Main 2024 Mathematics question

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 $\vec{r}=(-3 \hat{i}+2 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+5 \hat{k}), \lambda \in \mathbb{R}$ and $\vec{r}=(\hat{i}-2 \hat{j}+\hat{k})+\mu(-\hat{i}+3 \hat{j}+2 \hat{k}), \mu \in \mathbb{R}$ is :