Vector Algebra: JEE Main 2023 Mathematics question

Let O be the origin and the position vector of the point P be $- \widehat i - 2\widehat j + 3\widehat k$. If the position vectors of the points A, B and C are $- 2\widehat i + \widehat j - 3\widehat k,2\widehat i + 4\widehat j - 2\widehat k$ and $- 4\widehat i + 2\widehat j - \widehat k$ respectively, then the projection of the vector $\overrightarrow {OP}$ on a vector perpendicular to the vectors $\overrightarrow {AB}$ and $\overrightarrow {AC}$ is :