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 non - zero vector perpendicular to $\overrightarrow{x}$ and $\overrightarrow{y} \times \overrightarrow{z}$ and $\overrightarrow{b}$ is a non - zero vector perpendicular to $\overrightarrow{y}$ and $\overrightarrow{z} \times \overrightarrow{x}$ , then