gives the list representing the 2D unit vector at angle θ relative to the axis.


gives the list representing the 2D vector of length r at angle θ.


gives the result of starting from the point {x,y}, then going a unit distance at angle θ.


gives the result of starting from the point {x,y}, then going distance r at angle θ.


  • Unless explicitly given as a Quantity object, the angle θ is assumed to be in radians, counterclockwise starting from the axis. (Multiply by Degree to convert from degrees.)
  • AngleVector[{r,θ}] gives a vector that starts at {0,0}.
  • The arguments of AngleVector can be symbolic. They can also be Quantity objects.


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Basic Examples  (4)

Unit vector at angle θ:

Angles are assumed to be in radians:

Unit vector at angle 30°:

Use a Quantity angle instead:

General symbolic case:

Scope  (5)

Unit vector at angle Pi/3:

Use degrees:

Use Quantity angles in input:

Specify the norm of the vector:

Specify the origin of the vector:

Use Quantity values in input:

Properties & Relations  (4)

Reconstruct input:

For short displacements around a geo location, AngleVector approximates GeoDestination:

Move 10 kilometers with initial bearing of 40°:

Re-express that position in terms of a Cartesian frame centered at London:

The horizontal displacement vector in meters is approximately the following:

Folding of AngleVector can be used to move from a point along a sequence of {r,θ} displacements:

The same result can be achieved with AnglePath, using angles relative to the previous segment:

ListPolarPlot can be interpreted as a combination of AngleVector and ListPlot:

ListPolarPlot takes pairs {θi,ri}, but AngleVector takes pairs {r,θ}, so Reverse is needed:

Introduced in 2015