JEE Main 2023 Mathematics question on Three Dimensional Geometry

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