Let \(\vec{x},\vec{y}\) and \(\vec{z}\) be three vectors each of magnitude √2 and the angle between each pair of them is π/3 . If \(\vec{a}\) is a non-zero vector perpendicular to \(\vec{x}\) and \(\vec{y}\times \vec{z}\) and \(\vec{b}\) is a non-zero vector perpendicular to \(\vec{y}\) and \(\vec{z}\times\vec{x},\) then__

(A) \(\vec{b}=(\vec{b}.\vec{z})(\vec{z}-\vec{x})\)

(B) \(\vec{a}=(\vec{a}.\vec{y})(\vec{y}-\vec{z})\)

(C) \(\vec{a}.\vec{b}=-(\vec{a}.\vec{y})(\vec{b}.\vec{z})\)

(D) \(\vec{a}=(\vec{a}.\vec{y})(\vec{z}-\vec{y})\)