Q:

Sketching the vector field of -(r/||r||^3) where r = ?

Question: Sketch the vector field $$\vec F(x,y) = -\frac{\vec r}{||\vec r||^3}$$ in the plane, where $\vec r = \langle x,y\rangle$. Select all that apply.

A. The length of each vector is 1. 
B. The vectors decrease in length as you move away from the origin. 
C. All the vectors point toward the origin.
D. All the vectors point away from the origin. 
E. The vectors increase in length as you move away from the origin.

What am I exactly graphing? I know $\frac{\vec r}{||\vec r||}$ is just the unit vector and it may have something to do with the question, but I'm not exactly getting how to sketch the actual graph.

A:

This is how your vector field looks like.
Taken from http://www.lightandmatter.com/html_books/lm/ch22/ch22.html
That is, your vector field is the gravity forces field generated by a mass at the origin, up to a constant. To graph it it might help to note that the modulus of $F$ is a radial function and that the direction points to the origin...

