Definitions for unit vector
Random House Webster's College Dictionary
a vector having a length of one unit.
Category: Math, Physics
Origin of unit vector:
A vector with length 1.
In mathematics, a unit vector in a normed vector space is a vector whose length is 1. A unit vector is often denoted by a lowercase letter with a "hat", like this: . In Euclidean space, the dot product of two unit vectors is simply the cosine of the angle between them. This follows from the formula for the dot product, since the lengths are both 1. The normalized vector or versor of a non-zero vector u is the unit vector codirectional with u, i.e., where ||u|| is the norm of u. The term normalized vector is sometimes used as a synonym for unit vector. The elements of a basis are usually chosen to be unit vectors. Every vector in the space may be written as a linear combination of unit vectors. The most commonly encountered bases are Cartesian, polar, and spherical coordinates. Each uses different unit vectors according to the symmetry of the coordinate system. Since these systems are encountered in so many different contexts, it is not uncommon to encounter different naming conventions than those used here.
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