Each problem is worth 3 points.

1. Produce a plot of the vector field F(x,y) = xi - yj.
 
 

2. Produce a plot of the vector field F(x,y) = <x, y>.
 
 

3. Find a formula for a vector field where all the vectors point directly toward the origin and are of unit length.
 
 

4. [Based on McCallum et al. p. 331] Imagine a wide, steadily flowing river in the middle of which there is a fountain that spouts water horizontally in all directions. Suppose the vector field  represents the velocity field for the combined flow of the river and the fountain. Plot the vector field for several possible values of A and K (at least for K =1, A=1 and A=2). What is the significance of the constants A and K?
 
 

5. [Based on McCallum et al. p. 452] The vector field F(x,y) =  can be used to represent an idealized river flowing around a rock of radius 1. Plot the vector field.