How to make a vector field point by point?

Question

I have data for the components of the vectors at multiple points and want to plot something like a vector field from my points which obviously has to be done vector by vector because I do not know the equation of the field that I plot.

Is there a way I can plot the vectors vector by vector in 3D space?

Answer 1

Mathematica has a graphics primitive, Arrow, that will do what you ask. You may also need the graphics primitive Arrowheads to adjust the look of the arrowheads if you don't like the default arrowheads.

To demonstrate the use of Arrow, I will generate a set of tangents to function given by

f[x_] := 4 - x^2

vector[tail : {_, _}, slope_, length_: 1.] :=
  Module[{θ = ArcTan[slope]}, {tail, tail + length {Cos[θ], Sin[θ]}}]

tangetVectors = N @ Table[vector[{x, f[x]}, f'[x], .5], {x, Subdivide[-2, 2, 8]}]

{{{-2., 0.}, {-1.87873, 0.485071}}, 
 {{-1.5, 1.75}, {-1.34189, 2.22434}}, 
 {{-1., 3.}, {-0.776393, 3.44721}}, 
 {{-0.5, 3.75}, {-0.146447, 4.10355}}, 
 {{0., 4.}, {0.5, 4.}}, 
 {{0.5, 3.75}, {0.853553, 3.39645}}, 
 {{1., 3.}, {1.22361, 2.55279}}, 
 {{1.5,1.75}, {1.65811, 1.27566}}, 
 {{2., 0.}, {2.12127, -0.485071}}}

Now I will plot the curve 4 - x^2 along with the tangent vectors.

Plot[f[x], {x, -2, 2},
  AspectRatio -> 1,
  PlotStyle -> {Red, Dotted},
  PlotRangePadding -> {{Automatic, .2}, {.5, Automatic}},
  Epilog -> {AbsoluteThickness[1.5], Arrow /@ tangetVectors}]

If you don't want to put the vectors on plot, but only want to show the vectors themselves, use Graphics in place of Plot

Graphics[{AbsoluteThickness[1.75], Arrow /@ tangetVectors}]