r Figure 6: F (x, y) = ⟨− y, x⟩

This could be representing the counter-clockwise rotation of a wheel.

# Quadrant I

# Quadrant II

# Quadrant III

# Quadrant IV

Why do the vectors get longer as you move away from the origin?

# What’s going on at the origin?

# What’s happening along x-axis and why?

# What’s happening along y-axis and why?

3-Dimensional Vector Fields – hard to do by hand, you get to do 1 for HW Technology will come in handy here… Figures 10, 11, and 12 – you get a better feel for them if you can rotate them around. What’s the difference in formulas of Figures 10 and 11?

What’s the difference in the look of the vector fields? ( ) , , , 2 , F x y z y x = ⟨ − ⟩ r

y component is fixed (−2)

Compare the two vector fields. Can you see in Figure 11 that all of the vectors point in the general direction of the negative y-axis (because of the −2 )?

Maybe you can see it better on TEC 13.1 3D Vector Fields, Field 4. As I rotate to the xy or zy-plane you can see all vectors points in the general direction of the negative negative y-axis.