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

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