Let the lines l_1: (x+5)/3=(y+4)/1=(z-α)/-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…

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