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ABCDEF is a regular hexagon with point O...

ABCDEF is a regular hexagon with point O as centre. Find the value of `vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)`

Text Solution

Verified by Experts

From the diagram
`(vec(AB) =-vec(DE))(vec(BC)=-vec(EF))`
`vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)`
`=cancel(vec(AB)) +(cancel(vec(AB)) + cancel(vec(BC)) + cancel(vec(AD)) +(vec(AD) + vec(DE)) + (vec(AD) + cancel(vec(DE)) + cancel(vec(EF)))`
`=3vec(AD) =3(2vec(AO)) =6(vec(AO))`
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