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Consider the regular hexagon ABCDEF with...

Consider the regular hexagon ABCDEF with centre at O (origin).
Five forces `vec(AB), vec(AC), vec(AD), vec(AE), vec(AF)` act at the vertex A of a regular hexagon ABCDEF. Then their resultant is

A

` 3 vec(AO)`

B

`2 vec(AO)`

C

`4 vec(AO)`

D

`6 vec(AO)`

Text Solution

Verified by Experts

The correct Answer is:
D
Consider the regular hexagon ABCDEF with centre at O (origin)

`vec(AD) + vec(EB) + vec(FC) = 2 vec(AO) + 2 vec(OB) + 2 vec(OC)`
`" " = 2 ( vec(AO) + vec(OB) ) + 2 vec(OC)`
`" " = 2 vec(AB) + 2 vec(AB) `
`" " ( because vec(OC) = vec(AB))`
`" " = 4 vec(AB)`
`vecR = vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)`
`= vec(ED) + vec(AC) + vec(AD) + vec(AE) +vec(CD)`
`( because vec(AB) = vec(ED) and vec(AF)= vec(CD))`
`= ( vec(AC) + vec(CD)) + ( vec(AE) + vec(ED)) + vec(AD)`
`= vec(AD) + vec(AD) + vec(AD) = 3 vec(AD) = 6 vec(AO)`
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