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ABCDEF is a regular hexagon in the x-y p...

ABCDEF is a regular hexagon in the x-y plance with vertices in the anticlockwise direction. If `vecAB=2hati`, then `vecCD` is

A

`hati+sqrt(3)hatj`

B

`hati-sqrt(3)hatj`

C

`-hati+sqrt(3)hatj`

D

`sqrt(3)hati-hatj`

Text Solution

Verified by Experts

The correct Answer is:
C

`vecAB` is along the x-axis and BD is along the y-axis
`vec(AB) = 2veci rArr AB=BC=CD=………………=2`
From the figure, BM=BC`sin60^(@)`
`=2sin60^(@)`
`=sqrt(3)`
`therefore vec(BD) = 2sqrt(3)vecj`
`vec(BC) = BC cos60^(@)veci+BCsin60^(@)vecj`
`=veci+sqrt(3)vecj`
`therefore vec(CD) = vec(BD) = 2sqrt(3)vecj-(veci+sqrt(3)vecj)`
`=-veci+sqrt(3)vecj`
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