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 $\overrightarrow{\mathrm{OP}}$ on a vector perpendicular to the vectors $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{AC}}$ is