3d Geometry

The point of intersection \(\mathrm{C}\) of the plane \(8 x+y+2 z=0\) and the line joining the points \(\mathrm{A}(-3,-6,1)\) and \(\mathrm{B}(2,4,-3)\) divides the line segment \(\mathrm{AB}\) internally in the ratio \(\mathrm{k}: 1\). If \(\mathrm{a}, \mathrm{b}, \mathrm{c}(|\mathrm{a}|,|\mathrm{b}|,|\mathrm{c}|\) are coprime) are the direction ratios of the perpendicular from the point \(\mathrm{C}\) on the line \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}\), then \(|\mathrm{a}+\mathrm{b}+\mathrm{c}|\) is equal to ___________.