Consider the lines \( L_{1} \) and \( L_{2} \) given by:
\( L_{1}:\ \dfrac{x-1}{2}=\dfrac{y-3}{1}=\dfrac{z-2}{2} \)
\( L_{2}:\ \dfrac{x-2}{2}=\dfrac{y-2}{2}=\dfrac{z-3}{3} \)
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:
