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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
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.
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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