Let \( \vec{a} = \sqrt{7}\,\hat{i} + \hat{j} - \hat{k} \) and \( \vec{b} = \hat{j} + 2\hat{k} \). If \( \vec{r} \) is a vector such that \( \vec{r} \times \vec{a} + \vec{a} \times \vec{b} = \vec{0} \) and \( \vec{r} \cdot \vec{a} = 0 \), then \( |3\vec{r}|^{2} \) is equal to:
