# Intersection of plane and line

Geometry Level pending

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 $m:x-2=y=\frac{z-6}{5} ?$

×