Vector Algebra

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 :