Does the force of gravity equation include only one dimension?

Question

Been in a debate with someone who is claiming the force of gravity equation describes three dimensions. I was under the impression there is only one dimension relevant in the equation, that being the distance. Which view is correct?

Answer 1

The force acts in all three dimensions, the magnitude is 1 d. but $\vec{F}=-G\frac{Mm}{||r||^3}\vec{r}$ and $\vec{r}$ is 3d

Answer 2

Gravitational force, like all forces, is a vector comprising a direction in 3 dimensions and a magnitude. In some cases, the direction can be ignored, usually because in such a case the direction doesn't change, and the problem is effectively 1-dimensional.

Answer 3

In Newtonian gravity, the gravity depends on distance between two bodies depends on $r$, which is one dimension according to spherical coordinates. But in Euclidean system, it is three coordinates, $R^2 =x^2+y^2+z^2$, so gravity can be thought of as one or three according to your choice of coordinate system.