Let the unit vectors \(\vec{a}\) and \(\vec{b}\) be perpendicular to each other and the unit vector \(\vec{c}\) be inclined at an angle \(\theta\) to both \(\vec{a}\) and \(\vec{b}\). If \(\vec{c} = x\vec{a} + y\vec{b} + z(\vec{a} \times \vec{b})\), then
1
\(x = \cos{\theta}, y = \sin{\theta}, z = \cos{2\theta}\)
2
\(x = \sin{\theta}, y = \cos{\theta}, z = -\cos{2\theta}\)
3
\(x = y = \cos{\theta}, z^2 = \cos{2\theta}\)
4
\(x = y = \cos{\theta}, z^2 = -\cos{2\theta}\)