Let O be the origin and the position vector of the point P be - i -2 j +3 k. If the position vectors of the points A, B and C are -2 i + j -3 k, 2 i…

Let O be the origin and the position vector of the point P be $\displaystyle -\hat{i}-2 \hat{j}+3 \hat{k}$. If the position vectors of the points $\displaystyle \mathrm{A}, \mathrm{B}$ and C are $\displaystyle -2 \hat{i}+\hat{j}-3 \hat{k}, 2 \hat{i}+4 \hat{j}-2 \hat{k}$ and $\displaystyle -4 \hat{i}+2 \hat{j}-\hat{k}$ respectively, then the projection of the vector $\displaystyle \overrightarrow{O P}$ on a vector perpendicular to the vectors $\displaystyle \overrightarrow{A B}$ and $\displaystyle \overrightarrow{A C}$ is