Unit Vector -- From Wolfram MathWorld

Home » What Is The Unit Vector » Unit Vector -- From Wolfram MathWorld

Maybe your like

Search Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
  • Algebra
  • Vector Algebra
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

v^^=(v)/(|v|),

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

x_n^^=((partialr)/(partialx_n))/(|(partialr)/(partialx_n)|),

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

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

  • vector algebra
  • normalize (1,1)
  • normalize ((10.5, 3., 0.1) cross (0.02, 20.3, 0.1))

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.

Referenced on Wolfram|Alpha

Unit Vector

Cite this as:

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

Subject classifications

  • Algebra
  • Vector Algebra
Created, developed and nurtured by Eric Weisstein at Wolfram Research

Tag » What Is The Unit Vector