The point of intersection C of the plane 8 x+y+2 z=0 and the line joining the points A (-3,-6,1) and B (2,4,-3) divides the line segment AB…

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