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A pair of interactive plots are drawn to demonstrate the vector field
\(\langle -y,x,0\rangle\) in two different perspectives. At the top of the figure are sliders to change the angle of the plane drawn and the number of vectors plotted in the three dimensional plot. The top plot is a three dimensional plot with axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\text{.}\) A plane through the origin and the x-axis is shown in yellow. The angle this plane makes with the y-axis is changed by the slider above. Additionally, there is an array of vectors plotted representing the vector field. These vectors point in a circular pattern around the z-axis and are longer for locations farther from the z-axis. The second plot is a two dimensional plot of a vector field that shows arrows that show a pattern of clockwise rotation around the origin. As the angle of the plane in increased, the vector field becomes more stretched in the horizontal direction.