Let three vectors a, b and c be such that c is coplanar with a and b, a · c =7 and b is perpendicular to c, where a =- i + j + k and b =2 i + k, then…

Let three vectors $\displaystyle \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ be such that $\displaystyle \overrightarrow{\mathrm{c}}$ is coplanar with $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=7$ and $\displaystyle \overrightarrow{\mathrm{b}}$ is perpendicular to $\displaystyle \overrightarrow{\mathrm{c}}$, where $\displaystyle \overrightarrow{\mathrm{a}}=-\hat{i}+\hat{j}+\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{k}$, then the value of $\displaystyle 2|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}|^2$ is \_\_\_\_.