Let $\alpha$ be the plane passing through point $\mathrm { A } ( 1,2,3 )$ and perpendicular to the line $l : x - 1 = \frac { y - 2 } { - 2 } = \frac { z - 3 } { 3 }$.\\
When the intersection point of plane $\alpha$ and line $m : x - 2 = y = \frac { z - 6 } { 5 }$ is B, what is the length of segment AB? [3 points]\\
(1) $\sqrt { 19 }$\\
(2) $\sqrt { 17 }$\\
(3) $\sqrt { 15 }$\\
(4) $\sqrt { 13 }$\\
(5) $\sqrt { 11 }$