Unit Vector

An Unit Vector is a vector with unit length.

• Context:
  • It can (often) be a Spatial Vector.
• Example(s):
  • a Unit Normal Vector,
  • a Normalized Vector,
  • …
• Counter-Example(s):
  • a Zero Vector.
• See: Vector Normalization Function, Cross Product, Normed Vector Space, Vector Space, Vector (Geometry), Euclidean Space, Dot Product.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/unit_vector Retrieved:2015-2-7.
  • In 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 "hat": [math]\displaystyle{ {\hat{\imath}} }[/math] (pronounced "i-hat").

    The normalized vector or versor [math]\displaystyle{ \mathbf{\hat{u}} }[/math] of a non-zero vector u is the unit vector in the direction of u, i.e.,

     :[math]\displaystyle{ \mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|} }[/math]

    where ||u|| is the norm (or length) of u. The term normalized vector is sometimes used as a synonym for unit vector.

    Unit vectors are often chosen to form the basis of a vector space. Every vector in the space may be written as a linear combination of unit vectors.

    By definition, in an Euclidean space the dot product of two unit vectors is the cosine of the angle between them. In three-dimensional Euclidean space, the cross product of two orthogonal unit vectors is another unit vector, orthogonal to both of them.

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