Vector Algebra

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 :