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To answer this question, we first have to understand what is meant by "the two forces in the same interaction pair." This refers to the pair of forces by described by the third Newton's Law.
The third Newton's Law states that every action causes an equivalent reaction. That is, if one object acts on another with the force `vecF_1` , the second object must act back on the first object with the force equal in magnitude but opposite in direction:
`vecF_2 = -vecF_1`
These two forces are referred to as an "interaction pair". For example, if you push the door with some force in order to open it, the door will push back at your hand with equal force in the opposite direction.
From this definition of the interaction pair, it becomes apparent that the forces in the interaction pair cannot possibly be applied to the same object. They are always applied to two different objects interacting with each other. So, the two forces acting on you as you sit on a chair are not an interaction pair.
One force acting on you, downward, is the gravity. This is the force produced in the interaction between you and the Earth. The force paired with it by the third Newton's Law is the force acting on the Earth. You pull the Earth "up" with the force of the same magnitude with which the Earth pulls you "down".
The second force acting on you is the normal force with which chair pushes you up. It enables you to actually sit on a chair instead of falling through it. The interaction pair to this force is the force acting on the chair with which you are pushing down on it.
In a simple situation like this, because you are an equilibrium, the gravity and the normal force will balance each other, which means they will be equal an magnitude and opposite and direction, which makes it easy to confuse them with an interaction pair. However, this is not always the case. This is not the case if you are sitting on a chair in the accelerating elevator, or if the chair is on the slanted, instead of horizontal, floor.
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