The vertices $B$ and $C$ of a triangle $A B C$ lie on the line $\frac{x}{1}=\frac{1-y}{-2}=\frac{z-2}{3}$. The coordinates of $A$ and $B$ are ( $1,6,3$ ) and ( $4,9, \alpha$ ) respectively and C is at a distance of 10 units from B . The area (in sq. units) of $\triangle A B C$ is
