Mathematics - Vector Question with Solution | TestHub

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