Vector Algebra: JEE Main 2022 Mathematics question

Let $\overrightarrow a = {a_1}\widehat i + {a_2}\widehat j + {a_3}\widehat k$ ${a_i} > 0$, $i = 1,2,3$ be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of $\overrightarrow a$ on the vector $3\widehat i + 4\widehat j$ be 7. Let $\overrightarrow b$ be a vector obtained by rotating $\overrightarrow a$ with 90$^\circ$. If $\overrightarrow a$, $\overrightarrow b$ and x-axis are coplanar, then projection of a vector $\overrightarrow b$ on $3\widehat i + 4\widehat j$ is equal to: