For a regular hexagon ABCDEF shown below , prove that
`overset rarr(AB)+ overset rarr(AC) +overset rarr(AD) +oversetrarr(AE)+oversetrarr(AF) = 6oversetrarr(AO).`

Explanation

Using triangle law of vector addition , we have
`vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)`
`=vec(AB)+(vec(AD)+vec(DC))+vec(AD)+(vec(AD)+vec(DE))+vec(AF)`
`=3vec(AD)+vec(AB)+vec(DC)+vec(DE)+vec(AF)`
`=3vec(AD)+(vec(AB)+vec(DE))+(vec(DC)+vec(AF)) {:(( :. vec(AB)=-vec(DE)),(vec(DC)=-vec(AF))):}`
`=3(2vec(AO))+vecO+vec(O)`
`=6(vec(AO))`
Hence proved