Let O A B C be a parallelogram, O be the origin, A(2,4,-5) and C( b, 2,3). If P(a, a, a) and Q(9-a^2, 3, a-1), a ∈ N, are two points such that the…

Let $\displaystyle O A B C$ be a parallelogram, $\displaystyle O$ be the origin, $\displaystyle A(2,4,-5)$ and $\displaystyle C(\mathrm{~b}, 2,3)$. If $\displaystyle P(a, a, a)$ and $\displaystyle Q\left(9-a^2, 3, a-1\right), a \in \mathbb{N}$, are two points such that the projection of $\displaystyle \overrightarrow{O P}$ on $\displaystyle \overrightarrow{O B}$ is $\displaystyle 2$ and $\displaystyle \overrightarrow{O Q}$ makes acute angles with all three co-ordinate axes, then $\displaystyle |\overrightarrow{O B}|^2+|\overrightarrow{A C}|^2$ is equal to \_\_\_\_.