A unit vector is a vector of length 1 in a normed vector space. It is often denoted by a lowercase letter with a circumflex, or "hat," as in v̂ . The term direction vector is used to describe a unit vector being used to represent spatial direction and relative direction. 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 of unit vectors.
Some key points about unit vectors include:
- A unit vector has a magnitude of 1.
- The normalized vector û of a non-zero vector u is the unit vector in the direction of u.
- Unit vectors may be used to represent the axes of a Cartesian coordinate system.
- The dot product of two unit vectors is a scalar quantity, whereas the cross product of two arbitrary unit vectors results in a third vector orthogonal to both of them.
Unit vectors are useful in many areas of mathematics and physics, including linear algebra, calculus, and mechanics.
