Intersection of plane and line

Let $\alpha$ be the plane that contains the point $A(1, 2, 3)$ and is perpendicular to the line $l:x-1=\frac{y-2}{-2}=\frac{z-3}{3}.$ What is the length of the line segment $AB,$ where point B is the intersection of the plane $\alpha$ and the line $m:x-2=y=\frac{z-6}{5} ?$