Consider the lines \(L_1\) and \(L_2\) given by \[ \begin{aligned} & L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} …

Consider the lines \(L_1\) and \(L_2\) given by
\[
\begin{aligned}
& L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} \\
& L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}
\end{aligned}
\]

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 \(P Q\) is