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\( A, B, C \) are vertices of a triangle whose position vectors are \( \vec{a}, \vec{b} \) and \( \vec{c} \) respectively and \( G \) is the centroid of \( \triangle A B C \), then \( \overrightarrow{G A}+\overrightarrow{G B}+\overrightarrow{G C} \).
(A) \( \overrightarrow{0} \)
(B) \( \vec{a}+\vec{b}+\vec{c} \)
(C) \( \frac{\vec{i}+\vec{b}+\vec{c}}{3} \)
(D) \( \frac{\vec{a}-\vec{b}-\vec{c}}{3} \)
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