# Vectors or vector fields? (Notation, physics example)

This is from physics, however I need help with the math.

In the wikipedia-article of Newton's law of universal gravitation two forms are stated. One as vector form and one as a field.

I can't see any difference, aren't both vector fields?

Vector form: $$\mathbf{F}_{12}=-G\frac{m_1m_2}{\lvert \mathbf{r}_{12} \rvert^2} \underbrace{ \frac{\mathbf{r}_2-\mathbf{r}_1}{{\lvert \mathbf{r}_2-\mathbf{r}_1 \rvert}}}_\text{\mathbf{\hat r}_{12}}$$ where $\mathbf{F}_{12}$ is the force applied on object 2 due to object 1.

And gravitational field: $$\mathbf{g}(\mathbf{r}_{12})=-G\frac{m_1}{\lvert\mathbf{r}_{12} \rvert^2}\mathbf{\hat r}_{12}$$

What is the difference?

Isn't $\mathbf{F}_{12}$ just a abbreviation for $\mathbf{F}_{12}(\mathbf{r}_{12})$, i.e. a vector field?

• the wiki value seems satisfactory en.wikipedia.org/wiki/…, Note that $F(r)=mg(r)$. $g$ and $F$ are not the same at all, Not that the unites are different. If you are familiar with the electro static force, The gravitational field is an analog for the electric field. – sha Oct 9 '16 at 13:56