Triangle Area Side Length 3D

Let the co-ordinates of one vertex of △ABC 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 of △ABC is 21 sq. units and the line segment BC has length 2√21 units, then α2 is equal to _______.