3D-Geometry

Let unit vectors $\vec a$ and $\vec b$ be perpedicular to each other, and a unit vector $\vec c$ be inclined at an angle $\theta$ to both $\vec a$ and $\vec b$ . If $\vec c = \alpha \vec a + \beta \vec b + \gamma (\vec a \times \vec b)$ .

Precisely how many of the following equations are true?

(A) : $\alpha =\beta$ .
(B) : $1 - 2\alpha^2 = \gamma^2$ .
(C) : $\alpha^2 = \frac{1+\cos2\theta}2$ .
(D) : $\alpha^2 - \beta^2= \gamma^2$ .