Unit vector

vector of length one

A unit vector is any vector that is one unit in length. Unit vectors are often notated the same way as normal vectors, but with a mark called a circumflex over the letter (e.g. is the unit vector of .)[1][2]

To make a vector into a unit vector, one just needs to divide it by its length: .[3] The resulting unit vector will be in the same direction as the original vector.[4]

Standard basis vectorsEdit

Three common unit vectors are  ,   and  , referring to the three-dimensional unit vectors for the x-, y- and z-axes, respectively. These vectors are called the standard basis vectors of a 3-dimensional Cartesian coordinate system. They are commonly just notated as i, j and k.

They can be written as follows:  

For the  -th standard basis vector of a vector space, the symbol   (or  ) may be used.[4] This refers to the vector with 1 in the  -th component, and 0 elsewhere.

Related pagesEdit

ReferencesEdit

  1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-19.
  2. "Unit Vector". www.mathsisfun.com. Retrieved 2020-08-19.
  3. Weisstein, Eric W. "Unit Vector". mathworld.wolfram.com. Retrieved 2020-08-19.
  4. 4.0 4.1 "Unit Vectors | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-08-19.