# Newton's Third Law textbook -- question about the sign of a force

Mr Davis 97
Imagine that I am pushing on a wall. Then my textbook says that by Newton's third law, ##F_{AB} = F_{BA}##, where I am B and the wall is A. Isn't this wrong? Shouldn't it be that ##F_{AB} = -F_{BA}##?

Mentor
Shouldn't it be that ##F_{AB} = -F_{BA}##?
Sure, if they are using ##F## to represent the forces as vectors. Perhaps they were just talking about the magnitudes of the forces, which are equal.

Mr Davis 97
Sure, if they are using ##F## to represent the forces as vectors. Perhaps they were just talking about the magnitudes of the forces, which are equal.
Ah, I see. I guess it can get kind of ambiguous.

Mentor
Most introductory textbooks use boldface or arrows on top to denote vectors: $$\mathbf{F}_{AB} = -\mathbf{F}_{BA}\\{\vec F}_{AB} = - {\vec F}_{BA}$$ versus unadorned italics for magnitudes (scalars): $$F_{AB} = F_{BA}$$

Homework Helper
Newton's Third Law: For every force acting, there is an equal and opposite force acting. Equal in magnitude, opposite in direction.
Since the "opposite in direction" is often taken as a given, other descriptions generally concentrate on the magnitude, and so FAB = FBA.