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Consider the regular hexagon ABCDEF with...

Consider the regular hexagon ABCDEF with centre at O (origin).
Q. Five forces AB,AC,AD,AE,AF act at the vertex A of a regular hexagon ABCDEF. Then, their resultant is (a)3AO (b)2AO (c)4AO (d)6AO

A

3AO

B

2AO

C

4AO

D

6AO

Text Solution

Verified by Experts

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

`AD+EB+FC=2AO+2OB+2OC`
`=2(AO+OB)+2OC`
`=2AB+2AB" "[becauseOC=AB]`
`=4AB`
`R=AB+AC+AD+AE+AF`
`=ED+AC+AD+AE+CD" "[becauseAB=ED and AF=CD]`
`=(AC+CD)+(AE+ED)+AD`
`=AD+AD+AD=3AD=6AO`
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