Let c be a vector perpendicular to the vectors a = i + j - k and b = i +2 j + k. If c ·( i + j +3 k )=8 then the value of c ·( a × b ) is equal to \…

Let $\displaystyle \vec{c}$ be a vector perpendicular to the vectors $\displaystyle \overrightarrow{\mathrm{a}}=\hat{i}+\hat{j}-\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}+\hat{k}$. If $\displaystyle \overrightarrow{\mathrm{c}} \cdot(\hat{i}+\hat{j}+3 \hat{k})=8$ then the value of $\displaystyle \overrightarrow{\mathrm{c}} \cdot(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})$ is equal to \_\_\_\_.