Let \( PQR \) be a triangle such that \( \overrightarrow{PQ} = -2\hat{i} - \hat{j} + 2\hat{k} \) and \( \overrightarrow{PR} = a\hat{i} + b\hat{j} - 4\hat{k},\ a, b \in \mathbb{Z} \). Let \( S \) be the point on \( QR \), which is equidistant from the lines \( PQ \) and \( PR \). If \( |\overrightarrow{PR}| = 9 \) and \( \overrightarrow{PS} = \hat{i} - 7\hat{j} + 2\hat{k} \), then the value of \( 3a - 4b \) is ________.
