If \(\vec a, \vec b, \vec c\), are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is the centroid of the triangle, then what is \(\overrightarrow{AG}\) equal to ? .
1
\(\frac{\vec a + \vec b +\vec c}{3}\)
2
\(\frac{2\vec a - \vec b -\vec c}{3}\)
3
\(\frac{\vec b + \vec c - 2\vec a}{3}\)
4
\(\frac{\vec a - 2\vec b - 2\vec c}{3}\)