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Why don't the two forces of action and reaction balance each other ?

I imagine that although they are opposite forces, they have different points of application. Is this true?

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Yes.Thats true. For example the earth pull the moon and by Newtons 3rd law the moon also pull the earth. Forces are on two different object. if there is a body in between the line joining the earth's centre and the moon's centre then only the net force on the body(vector sum of forces by the moon and earth) can be zero(if the body is on the right place)because its on the same body.

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I just guess that 1 and 2 are two different bodies. So, the answer is in your question itself. F(1->2) is the force with which 1 acts on 2, and F(2->1) is the force with which 2 acts on 1. The forces don't act on the same body.

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