Let a = i +2 j + k, b =3( i - j + k ). Let c be the vector such that a × c = b and a · c =3. Then a ·(( c × b )- b - c ) is equal to:

Let $\displaystyle \overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+\hat{k}, \overrightarrow{\mathrm{~b}}=3(\hat{i}-\hat{j}+\hat{k})$. Let $\displaystyle \overrightarrow{\mathrm{c}}$ be the vector such that $\displaystyle \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=3$. Then $\displaystyle \overrightarrow{\mathrm{a}} \cdot((\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}})-\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}})$ is equal to: