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The mathematical representation of Newton’s third law of motion is let A be the body
exerting force F⃗ on the body B, then body B too exerts a force −F⃗ on body A, which is
given as:

F⃗ AB=−F⃗ AB

APPLICATIONS OF NEWTON’S THIRD LAW OF MOTION
A variety of action-reaction pairs are evident in nature. We have listed a few below and
they are as follows:

 A propulsion of fish through water is an example of action-reaction pair. A fish
makes use of its fins to push water backwards. This push serves to accelerate
the fish forwards. The size of the force on the water equals the size of the force
on the fish; the direction of the force on the water (backwards) is opposite the
direction of the force on the fish (forwards).

 The flight of the bird is an example of action-reaction pair. The wings of the bird
push the air downwards. The air pushes the air upwards.

 A swimmer pushes against the water, while the water pushes back on the
swimmer.
 Lift is created by helicopters by pushing the air down, thereby creating an upward
reaction force.
 Rock climbers pulling their vertical rope downwards so as to push themselves
upwards.