# 3D-Geometry

Geometry Level 3

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): $$\alpha^2 - \beta^2= \gamma^2$$.

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