Let `vec(alpha),vec(beta)` and `vec(gamma` be the unit vectors such that `vec(alpha)` and `vec(beta)` are mutually perpendicular and `vec(gamma)` is equally inclined to `vec(alpha)` and `vec(beta)` at an angle `theta`. If `vec(gamma)=xvec(alpha)+yvec(beta)+z(vec(alpha)xxvec(beta))`, then which one of the folllowing is incorrect?

Options

A. `z^2=1-2x^2`
B. `z^2=1-2y^2`
C. `z^2=1-x^2-y^2`
D. All the above

Answer

D