Let P be the plane passing through the points (5,3,0),(13,3,-2) and (1,6,2). For α ∈ N, if the distances of the points A (3,4, α) and B (2, α, a )…

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