Consider the lines ${\mathrm{L}}_1$  and  ${\mathrm{L}}_2$ given by
${\mathrm{L}}_1:\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}-3}{1}=\frac{\mathrm{z}-2}{2}$
${\mathrm{L}}_2:\frac{\mathrm{x}-2}{1}=\frac{\mathrm{y}-2}{2}=\frac{\mathrm{z}-3}{3}$
A line  ${\mathrm{L}}_3$ having direction ratios $\mathrm{1,\hspace{0.17em}-1,\hspace{0.17em}-2,}$  intersects   ${\mathrm{L}}_1$ and  ${\mathrm{L}}_2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is