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 …

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 \(-2 \hat{i}+\hat{j}-3 k, 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively, then the projection of the vector \(\overrightarrow{O P}\) on a vector perpendicular to the vectors \(\overrightarrow{A B}\) and \(\overrightarrow{A C}\) is

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