Five forces ` vec A B` , ` vec A C` , ` vec A D` , ` vec A E` and ` vec A F` act at the vertex of a regular hexagon `A B C D E Fdot` Prove that the resultant is `6 vec A O` , where `O` is the centre of heaagon.

Explanation

In a regular hexagon,


` vec{A B}+vec{A F}=vec{A O} `

` vec{A C}=vec{A B}+vec{B C}=vec{A B}+vec{A O} `

A E=A F+F E=A F+A D

` vec{A D}=2 vec{A O}`

A B+A C+A D+A E+A F

=A B+A F+A C+A F+A D

...