On an open ground, a motorist follows a track that turns to his left by an angle of `60^(@)` after every `500 m`. Starting from a given turn, The path followed by the motorist is a regular hexagon with side `500 m`, as shown in the given figure specify the displacement of the motorist

at the end of sixth turn.

Explanation

At III turn
Displacement `=vecOA+vecAB+vecBC+vecOC`
`=(500cos 60^(@)+500+500 cos 60^(@))` Form O to C
`=500xx(1)/(2)+500+500xx(1)/(2)=1000m` from O to C
Distance `=500+500+500=1500m therefore (|"Desplacement"|)/("Distance")=(1000)/(1500)=(2)/(3)`