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 :