Question

ABCDEF is a regular hexagon with point O as centre. The value of `vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)` is

Answer 1

From the diagram `vec(AB)=vec(-DE),vec(BC)=vec(-EF)`
`vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)`.
`=vec(AB)+(vec(AB)+vec(BC))+vec(AD)+(vec(AD)+vec(DE))+(vec(AD)+vec(DE)+vec(EF))`
`=vec(3AD)=3(vec(2AO))=6vec((AO))`