Prove that the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.

Explanation

`vec(AB)+vec(AC)=2vec(AD)`
`" "vec(BC)+vec(BA)=2vec(BE)`
`" "vec(CA)+vec(CB)=2vec(CF)`
Adding, we get
`" "(vec(AB)+vec(BA))+(vec(AC)+vec(CA))+(vec(BC)+vec(CB))=2(vec(AD)+vec(BE)+vec(CF))`
or `" "vec0+vec0+vec0=2(vec(AD)+vec(BE)+vec(CF))` or `" "vec(AD)+vec(BE)+vec(CF)=vec0`