Let O be the origin and the position vector of the point P be \(−\hat{i}−2\hat{j}+3\hat{k}.\) If the position vectors of…

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

[JEE Main 2023, 10 Apr (Shift 1)]