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given a hexagon of sides AB,BC,CD,DE,EF,FA with centre at O then prove that AB+AC+AD+AE+AF=6AO


given a hexagon of sides AB,BC,CD,DE,EF,FA with centre at O


then prove that AB+AC+AD+AE+AF=6AO


Grade:12

1 Answers

Ramesh V
70 Points
12 years ago
If R be the resultant, then
R=AB+AC+AD+AE+AF
=AB+(AD+DC)+AD+(AD+DE)+AF
Now AF and DC are two equal vectors in opposite directions and hence they cancel each other.
Similarly AB and DE cancel each other.
so R = 3A
=6AO
where is the mid. point of AD i. e. the centroid of the hexagon.

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