Plotting Vector Field: V=(xi+yj+zk)/\sqrt{}(x^2+y^2+z^2)

[mite]

How to plot this vector field on a graph
$$\stackrel{}{\rightarrow}$$
V=(xi+yj+zk)/$$\sqrt{}(x^2+y^2+z^2)$$

 

[Defennder]

Well, just ask yourself if you recognise the direction the vector field is pointing along at any given coordinate. In particular, consider the position vector of that coordinate as well. Doesn't this look familiar?

 

[HallsofIvy]

First obvious point: For any vector field, choose some points (x,y,z) ( because you can't plot all of them!), calculate the vector at that point, and plot it.

Now, look at Defennder's post for this specific vector field. $\sqrt{x^2+ y^2+ z^2}$ is a number and affects the length of the post. How does being closer or farther away from the origin affect the length of the vector? The direction is given entirely by xi+yj+zk. What direction would that be starting at the point (x,y,z)?