Relative velocity

-For two objects A and B moving with the uniform velocities V_A and V_B.
Relative velocity is defined as
V_BA=V_B-V_A
where V_BA is relative velocity of B relative to A

Similiary relative velocity of A relative to B
V_AB=V_A-V_B
Special cases.
For straight line motion,we can just add or subtract to get the relative velocity.
If the objects are moving in the same direction,relative velocity can be get by substracting other.If they are moving in opposite direction ,relative velocity will be get by adding the velocities example like train problems

For two dimensions motion,we will need to add or subtracting components along x & y direction to get the relative velocity
Suppose
v_A=v_xai + v_yaj
v_B=v_xbi + v_ybj

Relative velocity of B relative to A
=v_xbi + v_ybj -(v_xai + v_yaj)
=i(v_xb-v_xa) + j(v_yb-v_ya)

For three dimensions motion
v_A=v_xai + v_yaj +v_zaz
v_B=v_xbi + v_ybj + v_zbz

Relative velocity of B relative to A
=v_xbi + v_ybj + v_zbz -(v_xai + v_yaj +v_zaz)
=i(v_xb-v_xa) + j(v_yb-v_ya)+z(v_yb-v_ya)