(a) Find the equations of the diagonals of the parallelogram PQRS whose vertices are $\mathit{P}\left(4,2,-6\right),\mathit{Q}\left(5,-3,1\right),\mathit{R}\left(12,4,5\right)$ and $\mathit{S}\left(11,9,-2\right)$. Use these equations to find the point of intersection of diagonals.

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(b) A line $\mathit{l}$ passes through point $\left(-1,3,-2\right)$ and is perpendicular to both the lines $\frac{\mathit{x}}{1}=\frac{\mathit{y}}{2}=\frac{\mathit{z}}{3}$ and $\frac{\mathit{x}+2}{-3}=\frac{\mathit{y}-1}{2}=\frac{\mathrm{z}+1}{5}$. Find the vector equation of the line $\mathit{l}$. Hence, obtain its distance from origin.