Let $$\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$$, $$\vec{b} = 3\hat{i} + 4\hat{j} - 5\hat{k}$$ and a vector $$\vec{c}$$ be such that $$\vec{a} \times (\vec{b} + \vec{c}) + \vec{b} \times \vec{c} = \hat{i} + 8\hat{j} + 13\hat{k}$$. If $$\vec{a} \cdot \vec{c} = 13$$, then $$(24 - \vec{b} \cdot \vec{c})$$ is equal to _______