Let \( \vec{a} = \hat{i} + 4\hat{j} + 2\hat{k} \), \( \vec{b} = 3\hat{i} - 2\hat{j} + 7\hat{k} \) and \( \vec{c} = 2\hat{i} - \hat{j} + 4\hat{k} \). If a vector \( \vec{d} \) satisfies \( \vec{d} \times \vec{b} = \vec{c} \times \vec{b} \) and \( \vec{d} \cdot \vec{a} = 24 \), Then \( |\vec{d}|^{2} \) is equal to:
