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# Chapter 13 – Vector Calculus - page 4 / 6

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r Figure 6: F (x, y) = ⟨− y, x

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

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

# 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.

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