3d Geometry

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 \(\mathrm{P}(a, b, c)\) on \(l_{1}\) is nearest to the point \(\mathrm{Q}(-4,-3,2)\), then \(|a|+|b|+|c|\) is equal to