Consider the lines $L_{1}$ and $L_{2}$ given by $L_{1}:\ \dfrac{x-1}{2}=\dfrac{y-3}{1}=\dfrac{z-2}{2}$ $L_{2}:\ \dfrac{x-2}{1}=\dfrac{y-2}{2}=\dfrac{z-3}{3}$ A line $L_{3}$ having direction ratios $1,-1,-2$ intersects $L_{1}$ and $L_{2}$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is: