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based on an earlier version of the Wolfram Language.
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VectorPlot3D

VectorPlot3D[{vx, vy, vz}, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}]
generates a 3D vector plot of the vector field {vx, vy, vz} as a function of x, y and z.
VectorPlot3D[{field1, field2, ...}, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}]
plots several vector fields.
  • VectorPlot3D by default shows vectors from the vector field at a regular grid of 3D positions.
  • VectorPlot3D omits any vectors for which the vi etc. do not evaluate to real numbers.
  • VectorPlot3D has attribute HoldAll, and evaluates the fi only after assigning specific numerical values to x, y and z.
  • In some cases it may be more efficient to use Evaluate to evaluate the vi symbolically before specific numerical values are assigned to x, y and z.
BoxRatiosAutomaticratio of height to width
EvaluationMonitorNoneexpression to evaluate at every function evaluation
MethodAutomaticmethods to use for the plot
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotRange{Full,Full,Full}range of x, y, z values to include
PlotRangePaddingAutomatichow much to pad the range of values
RegionFunctionTrue&determine what region to include
VectorColorFunctionNonehow to color vectors
VectorColorFunctionScalingTruewhether to scale the argument to VectorColorFunction
VectorPointsAutomaticthe number or placement of vectors to plot
VectorScaleAutomaticthe scale and size of vectors to plot
VectorStyleAutomatichow to draw vectors
WorkingPrecisionMachinePrecisionprecision to use in internal computations
Plot a vector field:
Plot a vector field with arrows colored by the Norm of the field:
Plot with 3D arrows:
Plot a field with arbitrary three dimensional shapes:
Plot a field with arrows placed at random locations:
Color and scale the vectors based on the norm of the field:
Use 3D arrows:
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