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