Let $\vec{x}, \vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle bet

Question

Let $\vec{x}, \vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between each pair of them is $\pi / 3$. If $\vec{a}$ is a non-zero vector perpendicular to $\vec{x}$ and $\vec{y} 	imes \vec{z}$ and $\vec{b}$ is non-zero vector perpendicular to $\vec{y}$ and $\vec{z} 	imes \vec{x}$, then\

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(a, b, c)\