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Let us assume the hexagon be in I quadrant and one side( containing C) parallel to x-axis ( or i-axis). 
OG is vector = OC + CG. 
OC is vector = OA + CA. 
OA is vector =OB + BA 
BA , CA, CG have magnitudes predetermined by sides and angles predetermined by orientation of hexagon. 
then use theorum on vector transformations to generalise the result.
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