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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+3hatj`

B

`hati9+2hatj`

C

`-hati+sqrt(3)hatj`

D

none of these

Text Solution

Verified by Experts

AB is along the X-axis and BD is along the Y-axis.
`AB=2hatiimpliesAB=BC=CD=` . . . . .=2

From the figure, BC=BC`sin60^(@)=2sin60^(@)=sqrt(3)`
`thereforeBD=2sqrt(3)hatj`
`BC=BCcos60^(@)hati+BCsin60^(@)hatj=hati+sqrt(3)hatj`
`CD=BD-BC=2sqrt(3)hatj-(hati+sqrt(3)hatj)=-hati+sqrt(3)hatj`
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