Let the lines \(l_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}\) and \(l_2: 3 x+2 y+z-2=0=x-3 y+2 z-13\) be coplan…

Let the lines \(l_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}\) and \(l_2: 3 x+2 y+z-2=0=x-3 y+2 z-13\) be coplanar. If the point \(P(a, b, c)\) on \(l_1\) is nearest to the point \(Q(-4,-3,2)\), then \(|a|+|b|+|c|\) is equal to

[JEE Main 2023, 12 Apr (Shift 1)]