Let \( \vec{a}=\hat{i}+2\hat{j}-3\hat{k} \) and \( \vec{b}=2\hat{i}-3\hat{j}+5\hat{k} \). If \( \vec{r}\times \vec{a}=\vec{b}\times \vec{r},\ \vec{r}\cdot(\alpha \hat{i}+2\hat{j}+\hat{k})=3 \) and \( \vec{r}\cdot(2\hat{i}+5\hat{j}-\alpha \hat{k})=-1, \ \alpha \in \mathbb{R} \), then the value of \( \alpha+|\vec{r}|^{2} \) is equal to:
