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Plot the following vector fields in the x-y plane; For each vector field, investigate the following questions that get at the nature of the vector field.

(a) How the magnitude changes when (x, y) → 0 and (x, y) → ∞

(b) How a particle would move if dropped at any given point? Choose 2-3 points and describe and/or draw their trajectories.

(i) Indicate any special points or axis that may be exceptions to part (b) such as any undefined points

(c) Indicate the sign (+ or -) of the divergence and curl in 2 regions. You do not have to choose the same regions for the divergence and curl.

1. F(x, y) = x^i + y^j

2. F(x, y) =− yi^ + x j^

3. F(x, y) = i ︿ + j ︿

4. F(x, y) = − xi^ + −y j ^

5. F(x, y) = − yi − y j ^

 

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