Mathematics Question from JEE Main 2023 · 1 February, Shift 2

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