Let \( \vec{a} = \hat{i} - 2\hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + \hat{j} + \hat{k} \) and \( \vec{c} \) be a vector such that \( \vec{a} + (\vec{b} \times \vec{c}) = \vec{0} \) and \( \vec{b} \cdot \vec{c} = 5 \). Then, the value of \( 3(\vec{c} \cdot \vec{a}) \) is equal to ______.
