Vector Algebra: JEE Main 2023 Mathematics question

The vector $\overrightarrow a = - \widehat i + 2\widehat j + \widehat k$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $\overrightarrow b$. Then the projection of $3\overrightarrow a + \sqrt 2 \overrightarrow b$ on $\overrightarrow c = 5\widehat i + 4\widehat j + 3\widehat k$ is :