How to plot a vector field from a given function

[Ted123]

Homework Statement

[PLAIN]http://img84.imageshack.us/img84/5273/questionm.png

The Attempt at a Solution

How do I go about plotting this?

 

[vela]

At each point in the xy-plane, draw a vector with its tail on the point. For example, for the point r=(1,0,0), you have F(r)=(1,0,0), so you'd draw an arrow that starts at r and extends one unit horizontally to the right.

 

[Ted123]

At each point in the xy-plane, draw a vector with its tail on the point. For example, for the point r=(1,0,0), you have F(r)=(1,0,0), so you'd draw an arrow that starts at r and extends one unit horizontally to the right.

Does $r = | \textbf{r}| = \sqrt{x^2+y^2+z^2}$ (i.e. the length of the vector)?

So for e.g. $\textbf{r} = (2,1,0)$ does $r=\sqrt{5}$ and so $\textbf{F}(\textbf{r}) = (\frac{2}{\sqrt{5}} , \frac{1}{\sqrt{5}} , 0)$ ?

How many vectors are there to draw? (all the combinations of (m,n) such that $m,n=0,\pm 1, \pm 2$ )?

 

[vela]

I'd assume that's what r means. You could always ask your instructor for clarification.

You should have 24 vectors to draw since m and n can each be one of five values, but you're omitting m=n=0.