Let \( \vec{a} = \hat{i} - 3\hat{j} + 7\hat{k} \), \( \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{c} \) be a vector such that \( (\vec{a} + 2\vec{b}) \times \vec{c} = 3 (\vec{c} \times \vec{a}) \). If \( \vec{a} \cdot \vec{c} = 130 \), then \( \vec{b} \cdot \vec{c} \) is equal to \( \_\_\_\_\_\_\_\_\_\_\_ \).
