If a =α i +β j +3 k, b =-β i -α j - k and c = i -2 j - k such that a · b =1 and b · c =-3, then 1/3(( a × b ) · c ) is equal to \ \ \ \.

If $\displaystyle \vec{a}=\alpha \hat{i}+\beta \hat{j}+3 \hat{k}$, $$\begin{aligned} & \overrightarrow{\mathrm{b}}=-\beta \hat{i}-\alpha \hat{j}-\hat{k} \text { and } \\ & \overrightarrow{\mathrm{c}}=\hat{i}-2 \hat{j}-\hat{k} \end{aligned} $$ such that $\displaystyle \vec{a} \cdot \vec{b}=1$ and $\displaystyle \vec{b} \cdot \vec{c}=-3$, then $\displaystyle \frac{1}{3}((\vec{a} \times \vec{b}) \cdot \vec{c})$ is equal to \_\_\_\_.