Let a = i -3 j +7 k, b =2 i - j + k and c be a vector such that ( a +2 b ) × c =3( c × a ). If a · c =130, then b · c is equal to ____.

Let $\displaystyle \overrightarrow{\mathrm{a}}=\hat{i}-3 \hat{j}+7 \hat{k}, \overrightarrow{\mathrm{~b}}=2 \hat{i}-\hat{j}+\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ be a vector such that $\displaystyle (\overrightarrow{\mathrm{a}}+2 \overrightarrow{\mathrm{~b}}) \times \overrightarrow{\mathrm{c}}=3(\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}})$. If $\displaystyle \vec{a} \cdot \vec{c}=130$, then $\displaystyle \vec{b} \cdot \vec{c}$ is equal to $\displaystyle \_\_\_\_$.