Let the co-ordinates of one vertex of A B C be A(0,2, α) and the other two vertices lie on the line (x+α)/5=(y-1)/2=(z+4)/3. For α ∈ Z, if the area…

Let the co-ordinates of one vertex of $\displaystyle \triangle A B C$ be $\displaystyle A(0,2, \alpha)$ and the other two vertices lie on the line $\displaystyle \frac{x+\alpha}{5}=\frac{y-1}{2}=\frac{z+4}{3}$. For $\displaystyle \alpha \in \mathbb{Z}$, if the area of $\displaystyle \triangle A B C$ is $\displaystyle 21$ sq. units and the line segment $\displaystyle B C$ has length $\displaystyle 2 \sqrt{21}$ units, then $\displaystyle \alpha^2$ is equal to $\displaystyle \_\_\_\_$.