If $\overrightarrow a,\overrightarrow b$ are mutually $\perp$ unit vectors and the vectors $x\overrightarrow a+x\overrightarrow b+z(\overrightarrow a\times\overrightarrow b ),\:\:\overrightarrow a+(\overrightarrow a\times\overrightarrow b),\:\:and\:\:z\overrightarrow a+z\overrightarrow b+y(\overrightarrow a\times\overrightarrow b)$ lie in a plane then $Z$ is ?

Question

$\begin {array} {1 1} (A)\;A.M \: of \: x \: and \: y & \quad (B)\;G.M \: of \: x \: and \: y \\ (C)\;H.M \: of \: x \: and \: y & \quad (D)\;Equal \: to \: zero \end {array}$