Suppose you are reding a bike with a speed of `10 m s^(-1)` due relative to a person `A` person `A` who is walking on the ground towards east. If your friend `B` walking on the ground due west measures you speed as `15 m s^(-1)`, find the relative velocitur between two refence frames `A` and `B`.

Explanation

Taking east direction as positive (positive east)
`vec v_(you), A=10 m s^(-1)`
`vec v _(A,B)=vec v_(A,you)+ vec _(you,B)` …(i)
`vec v_(you)=vec v_(you,A)+vec v A` ….(ii)
As the direction of `vec v_(you,A)` and `vec vA` is both toward east. Hence, uour direction should be toward east.
`vec v_(you,B)=vec v_(you)-vec vB` ..(iii)
As `B` is moving toward west and you and you are moving towards east. Hence, your direction w.r.t `B` should be toward east. ` vec _(you,B)=15 m s^(-1)` ("towrds eads")
Now from (i), `vec v,B)=-10+5 m s^(-1)`
Hence, velocity `A` w.r.t `B` will be `5 m s^(-1)` toward east.