Unit vector

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. formula_1 is the unit vector of formula_2.)
To make a vector into a unit vector, one just needs to divide it by its length: formula_3. The resulting unit vector will be in the same direction as the original vector.
Standard basis vectors.
Three common unit vectors are formula_4, formula_5 and formula_6, 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:
formula_7
For the formula_8-th standard basis vector of a vector space, the symbol formula_9 (or formula_10) may be used. This refers to the vector with 1 in the formula_8-th component, and 0 elsewhere.