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Calculus 3: Vector fields, divergence, and curl

Consider the vector field F(x,y)=yi+xjF(x,y) = -yi + xj. To get an idea of how this vector field looks, plug in a few coordinates and plot the resultant vectors.

Use the computer to plot the vector field F(x,y)=yi^xj^\mathbf{F}(x, y) = y\hat{i} - x\hat{j} and observe the pattern that emerges for different densities and length scalings.

Sketch the vector field F(x,y)=xi^+yj^\mathbf{F}(x, y) = x\hat{i} + y\hat{j} and describe the starburst pattern that you observe.

Find the force vector at a given point (x, y) in a 2D rotational vector field given by F(x,y)=(y,x)F(x, y) = (y, -x).