Let \( \vec{a} = 2\hat{i} - 3\hat{j} + \hat{k} \), \( \vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k} \) and a vector \( \vec{c} \) be such that \( (\vec{a} - \vec{c}) \times \vec{b} = -18\hat{i} - 3\hat{j} + 12\hat{k} \) and \( \vec{a} \cdot \vec{c} = 3 \). If \( \vec{b} \times \vec{c} = \vec{d} \), then \( \left| \vec{a} \cdot \vec{d} \right| \) is equal to:
