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

[JEE Main 2023, 25 Jan (Shift 1)]