Built-in Mathematica Symbol

VectorPlot3D

VectorPlot3D[{v_x, v_y, v_z}, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}]
generates a 3D vector plot of the vector field {v_x, v_y, v_z} as a function of x, y and z.

VectorPlot3D[{field₁, field₂, ...}, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}]
plots several vector fields.

MORE INFORMATION

VectorPlot3D by default shows vectors from the vector field at a regular grid of 3D positions.

VectorPlot3D omits any vectors for which the v_i etc. do not evaluate to real numbers.

VectorPlot3D treats the variables x, y and z as local, effectively using Block.

VectorPlot3D has attribute HoldAll, and evaluates the f_i 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 v_i symbolically before specific numerical values are assigned to x, y and z.

VectorPlot3D has the same options as Graphics3D, with the following additions and changes:

BoxRatios	Automatic	ratio of height to width
EvaluationMonitor	None	expression to evaluate at every function evaluation
Method	Automatic	methods to use for the plot
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotRange	{Full,Full,Full}	range of x, y, z 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