Let $$\overrightarrow{x}, \overrightarrow{y}$$ and $$\overrightarrow{z}$$ be three vectors each of magnitude $$\sqrt 2$$ and the angle between each pair of them is $$\frac{\pi}{3}.$$ If $$\overrightarrow{a}$$ is a nonzero vector perpendicular to $$\overrightarrow{x}$$ and $$\overrightarrow{y} \times \overrightarrow{z}$$ and $$\overrightarrow{b}$$ is a nonzero vector perpendicular to $$\overrightarrow{y}$$ and $$\overrightarrow{z} \times \overrightarrow{x}$$, then