Let a = i -α j +β k, b =3 i +β j -α k and c =-α i -2 j + k, where α and β are integers. If a · b =-1 and b · c =10, then ( a × b ) · c is equal to \…

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