13.1 Visualizing Vector Fields

Sketching Vector Fields w Mathematica

Sketching a vector field in 2 dimensions: (OverVector[F])=y (OverHat[i])-x (OverHat[j])

VectorPlot[{y,-x},{x,-4,4},{y,-4,4}]

Does Mathematica display the correct length of the vectors? Use the following plot to decide: Calculate the length of at least one vector and compare to your estimate of the length that Mathematica plots.

VectorPlot[{1,0.5*y},{x,-1,3},{y,-1,3}]

If it *doesn’t* display the correct length, what other information does it use to hint at the relative length?

Vector fields in 3 dimensions:

VectorPlot3D[{y,z,x},{x,-4,4},{y,-4,4},{z,-4,4}]

VectorPlot3D[{x,y,z},{x,-4,4},{y,-4,4},{z,-4,4}]