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 \( \overrightarrow{OP} \) on a vector perpendicular to the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{AC} \) is:
