Mathematics Question from JEE Main 2023 · 11 April, Shift 2

Let $P$ be the plane passing through the points $(5, 3, 0)$, $(13, 3, -2)$, and $(1, 6, 2)$. For $\alpha \in \mathbb{N}$, if the distances of the points $A(3, 4, \alpha)$ and $B(2, \alpha, a)$ from the plane $P$ are $2$ and $3$ respectively, then the positive value of $a$ is: