1. MathematicsIn mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in 𝐯̂ (pronounced "v-hat"). The term normalized vector is sometimes used as a synonym for unit vector. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., 𝐮̂=𝐮‖𝐮‖=(u1‖𝐮‖,u2‖𝐮‖,...,un‖𝐮‖) where ‖u‖ is the norm (or length) of u and 𝐮=(u1,u2,...,un). The proof is the following: ‖𝐮̂‖=u1u12+...+un22+...+unu12+...+un22=u12+...+un2u12+...+un2=1=1 A unit vector is often used to represent directions, such as normal directions. Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination form of unit vectors. == Orthogonal coordinates == === Cartesian coordinates === Unit vectors may be used to represent the axes of a Cartesian coordinate system. For instance, the standard unit vectors in the... from wikipedia.org