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

Let O be the origin and the position vector of the point P be \(−\overset{^}{i}−2\overset{^}{j}+3\overset{^}{k}.\) If the position vectors of the points A, B and C are \(−2\overset{^}{i}+\overset{^}{j}−3\overset{^}{k},\) \(2\overset{^}{i}+4\overset{^}{j}−2\overset{^}{k}\) and \(−4\overset{^}{i}+2\overset{^}{j}−\overset{^}{k}\) 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)]