If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}|=1,|\vec{b}|=2~and\vec{a}\cdot\vec{b}=\sqrt{3}\) then the angle between \(2\vec{a}\) and \(-\vec{b}\) is:
A. \(\frac{\pi}{6}\)
B. \(\frac{\pi}{3}\)
C. \(\frac{5\pi}{6}\)
D. \(\frac{11\pi}{6}\)
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