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

Let $\displaystyle \overrightarrow{\mathrm{a}}=\hat{i}+\hat{j}+\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{j}-\hat{k}$. If $\displaystyle \overrightarrow{\mathrm{c}}$ is a 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 $\displaystyle \overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})$ is equal to :