Unit Vector

A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector v^^ having the same direction as a given (nonzero) vector v is defined by

where |v| denotes the norm of v, is the unit vector in the same direction as the (finite) vector v. A unit vector in the x_n direction is given by

where r is the radius vector.

When considered as the ith basis vector of a vector space, a unit vector may be written e_i (or e^->_i).

See also

Direction, Norm, Radius Vector, Vector, Zero Vector

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References

Jeffreys, H. and Jeffreys, B. S. "Direction Vectors." §2.034 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 64, 1988.Stephens, M. A. "The Testing of Unit Vectors for Randomness." J. Amer. Stat. Assoc. 59, 160-167, 1964.

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Unit Vector

Cite this as:

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

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