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## Homework Statement

I am currently reading about Newton's Law of Universal Gravitation and I am so confused as to why there is a negative sign in front of the equation Fg = (G* m1m2)/r^2.

## Homework Equations

Fg = (G* m1m2)/r^2

There is a vector form of the magnitude of the gravitational force

**F**12 = - ((G*m1m2)/r^2 )

**r**12

**F**12 = force exerted by object 1 on object 2

G = 6.67 x 10^-11 N⋅m^2 /kg^2

m1 = mass of object 1

m2 = mass of object 2

r = distance between the centers of masses of objects 1 and 2

## The Attempt at a Solution

The text states that the negative sign indicates that object 1 is attracted toward object 2 and that through Newton's 3rd law, the force exerted by m2 on m1,

**F**21 is equal in magnitude to

**F**12 but opposite in direction. Therefore, these forces form an action-reaction pair⇒

**F**21=-

**F**12.

So if

**F**12= (G*m1m2)/r^2, then

**F**21 = -(G*m1m2)/r^2

I know that force is a vector quantity, but I am not sure when to use the vector form; and why is the vector form negative? I am so confused...Could anyone please help me understand this mathematically and conceptually?