Question
Prove that the sum of all the v ectors from the centre of a regular octagon to its vertices is the zero vector.
Solution
Let O be the centre of regular octagon ABCDEFGH.
O is mid-point of each of the diagonals AE, BF, CG and DH.
O is mid-point of AE.
...(1)
Similarly 
...(2)
...(3)
...(4)
Adding (1), (2), (3) and (4). we get,
Hence the result.
