JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 88

Let OABC 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 projection of $\overrightarrow{OP}$ on $\overrightarrow{OB}$ is 2 and $\overrightarrow{OQ}$ makes acute angles with all three co-ordinate axes, then $|\overrightarrow{OB}|^2+|\overrightarrow{AC}|^2$ is equal to _______.