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