Let \( \vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k} \) and \( \vec{b} = 7\hat{i} + \hat{j} - 6\hat{k} \). If \( \vec{r} \times \vec{a} = \vec{r} \times \vec{b}, \ \vec{r} \cdot (\hat{i} + 2\hat{j} + \hat{k}) = 3 \), then \( \vec{r} \cdot (2\hat{i} - 3\hat{j} + \hat{k}) \) is equal to:
