Let → a and → b be two unit vectors such that → a . → b = 0 . For...

Let $\overset{\to}{a} and$\overset{\to}{b}$be two unit vectors such that$\overset{\to}{a} . \overset{\to}{b} = 0 .$For some$x, y \in R,$let$\overset{\to}{c} = x\overset{\to}{a} + y\overset{\to}{b} + \left(\overset{\to}{a} \times \overset{\to}{b}\right) .$If \left|\overset{\to}{c}\right| = 2$ and the vector $\overset{\to}{c}$ is inclined at the same angle $\alpha$ to both $\overset{\to}{a} and \overset{\to}{b} ,$ then the value of $8\cos^{2} \alpha$ is