Five forces and 
and 
act at the vertex of a regular hexagon ABCDEF. Prove that the resultant is 6 
where O is the centre of hexagon.
Given a regular hexagon ABCDEF with O as the centre of the hexagon as shown in figure below
To prove 
We know that centre O of the hexagon bisects the diagonals
∴, 
, 
Consider ΔABO and apply triangle law of vector, we get
And consider ΔACO and apply triangle law of vector, we get
And consider ΔAEO and apply triangle law of vector, we get
And consider ΔAFO and apply triangle law of vector, we get
Now,
Substitute the corresponding values from eqn(i) to eqn(v) in above eqn, we get
[from eqn(i)]
[as 
and 
]
Hence 
Therefore the resultant of the five forces 
and 
is 
Hence proved
10