IN the figure shown ,ABCDEF is a regular hexagon . What is the of `AB+AC+AD+AE+AF`?

Options

A. `2vec(AO)`
B. `2vec(AO)`
C. `6vec(AO)`
D. 0

Answer

C

Explanation

`vec(AB)+vec(AF)=vec(AO)rArr vec(AB)=vec(AO)-vec(AF)`
`vec(AC)=vec(AB)+vec(AO),vec(AD)=2vec(AO),vec(AE)=vec(AO)+vec(AF)`

Now, `vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)`
`=5vec(AO)+vec(AB)+vec(AF)=5vec(AO)+vec(AO)=6vec(AO)`