Question

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+3hatj`
D. none of these

Answer 1

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`