Let \( \vec{a} = 3\hat{i} + \hat{j} - \hat{k} \) and \( \vec{c} = 2\hat{i} - 3\hat{j} + 3\hat{k} \). If \( \vec{b} \) -is a vector such that \( \vec{a} = \vec{b} \times \vec{c} \) -and \( |\vec{b}|^2 = 50 \), then \( \left| 72 - |\vec{b} + \vec{c}|^2 \right| \) is equal to ______.
