Let the lines $\ell_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}$ and $\ell_2: 3 x+2 y+z-2=0=x-3 y+2 z-13$ be coplanar. If the point $\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})$ on $\ell_1$ is nearest to the point $\mathrm{Q}(-4,-3,2)$, then $|\mathrm{a}|+|\mathrm{b}|+|\mathrm{c}|$ is equal to-