Vector Algebra

Let a vector ${\overrightarrow a }$ be coplanar with vectors $\overrightarrow b = 2\widehat i + \widehat j + \widehat k$ and $\overrightarrow c = \widehat i - \widehat j + \widehat k$. If ${\overrightarrow a}$ is perpendicular to $\overrightarrow d = 3\widehat i + 2\widehat j + 6\widehat k$, and $\left| {\overrightarrow a } \right| = \sqrt {10}$. Then a possible value of [\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow d } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow c } & {\overrightarrow d } \cr } ] is equal to :