Three Dimensional Geometry: JEE Main 2023 Mathematics question

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 ___________.