If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c $$ is unit vector perpendicular to $$\overrightarrow a $$ and coplanar with $$\overrightarrow a $$ and $$\overrightarrow b $$, then unit vector $$\overrightarrow d $$ perpendicular to both $$\overrightarrow a $$ and $$\overrightarrow c $$ is

If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow \gamma = \widehat i + \widehat k$$ then the maximum value of $$\left[ {\overrightarrow \alpha \overrightarrow \beta \overrightarrow \gamma } \right]$$ is