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 ^