Let $\vec{a}=\hat{i}-\alpha \hat{j}+\beta \hat{k}, \vec{b}=3 \hat{i}+\beta \hat{j}+\alpha \hat{k}$ and $\vec{c}=-\alpha \hat{i}+2 \hat{j}+\hat{k}$, where $\alpha$ and $\beta$ are integers. If $\vec{a} \cdot \vec{b}=-1$ and $\vec{b} \cdot \vec{c}=-10$, then $(\vec{a} \times \vec{b}) \cdot \vec{c}$ is-equal to $\_\_\_\_$ _