BUILT-IN MATHEMATICA SYMBOL

# VectorPlot

VectorPlot[{vx, vy}, {x, xmin, xmax}, {y, ymin, ymax}]
generates a vector plot of the vector field as a function of x and y.

VectorPlot[{{vx, vy}, {wx, wy}, ...}, {x, xmin, xmax}, {y, ymin, ymax}]
plots several vector fields.

## Details and OptionsDetails and Options

• VectorPlot by default shows vectors from the vector field at a regular grid of positions.
• VectorPlot omits any vectors for which the etc. do not evaluate to real numbers.
• VectorPlot treats the variables x and y as local, effectively using Block.
• VectorPlot has attribute HoldAll, and evaluates the , etc. only after assigning specific numerical values to x and y.
• In some cases it may be more efficient to use Evaluate to evaluate the , etc. symbolically before specific numerical values are assigned to x and y.
• VectorPlot has the same options as Graphics, with the following additions and changes:
•  AspectRatio 1 ratio of height to width EvaluationMonitor None expression to evaluate at every function evaluation Frame True whether to draw a frame around the plot FrameTicks Automatic frame tick marks Method Automatic methods to use for the plot PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotLegends None legends to include PlotRange {Full,Full} range of x, y values to include PlotRangePadding Automatic how much to pad the range of values RegionFunction True& determine what region to include VectorColorFunction None how to color vectors VectorColorFunctionScaling True whether to scale the argument to VectorColorFunction VectorPoints Automatic the number or placement of vectors to plot VectorScale Automatic the scale and size of vectors to plot VectorStyle Automatic how to draw vectors WorkingPrecision MachinePrecision precision to use in internal computations
• The arguments supplied to functions in RegionFunction and VectorColorFunction are x, y, , , Norm[{vx, vy}].

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Plot the vector field :

 Out[1]=

Plot multiple vector fields:

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