Let \( \vec{a} = 2\hat{i} + 7\hat{j} - \hat{k} \), \( \vec{b} = 3\hat{i} + 5\hat{k} \) and \( \vec{c} = \hat{i} - \hat{j} + 2\hat{k} \). Let \( \vec{d} \) be a vector which is perpendicular to both \( \vec{a} \) and \( \vec{b} \), and \( \vec{c} \cdot \vec{d} = 12 \). Then \( (-\hat{i} + \hat{j} - \hat{k}) \cdot (\vec{c} \times \vec{d}) \) is equal to:
