The perpendicular distance from origin to the plane passing through the points $2\overline{\mathrm{j}}-2\overline{\mathrm{j}}+\overline{\mathrm{k}},3\overline{\mathrm{i}}+2\overline{\mathrm{j}}-\overline{\mathrm{k}},3\overline{\mathrm{i}}-\overline{\mathrm{j}}-2\overline{\mathrm{k}}$ is

$\mathrm{eq} \mathrm{of} \mathrm{plane} \left|\begin{array}{ccc}\mathrm{x}-\mathrm{z}& \mathrm{y}+\mathrm{z}& \mathrm{z}-1\\ 1& 4& -2\\ 1& 1& -3\end{array}\right|=0$

$\begin{array}{rcl}(\mathrm{x}-2) (-10)-(\mathrm{y}+2) (-1)+(\mathrm{z}-1) (-3)& =& 0\\ -10\mathrm{x}+20+\mathrm{y}+2-3\mathrm{z}+3& =& 0\\ 10\mathrm{x}-\mathrm{y}+3\mathrm{z}-25& =& 0\end{array}$

$\perp$ distance $=\frac{25}{\sqrt{100+1+9}}=\frac{25}{\sqrt{110}}$