The term "polar vector" has two different definitions.

In elementary math, the term "polar vector" is used to refer to a representation of a vector as a vector magnitude (length) and angle, which is equivalent to specifying its endpoints in polar coordinates (illustrated above).

In physics, a polar vector transforms as an ordinary vector under an orthogonal transformation, without the extra determinant factor that characterizes a pseudovector. When a physical configuration is inverted relative to a fixed right-handed coordinate system, a polar vector reverses direction whereas a pseudovector does not. This is distinct from a passive change of coordinate axes. Examples of polar vectors include the radius vector , the velocity vector , momentum , and force . The cross product of two polar vectors is a pseudovector.

See also

Cylindrical Coordinates, Polar Angle, Polar Coordinates, Polar Plot, Pseudovector, Spherical Coordinates, Vector

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 128-129, 1985.

Referenced on Wolfram|Alpha

Polar Vector

Cite this as:

Weisstein, Eric W. "Polar Vector." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PolarVector.html

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