Unit Vector - Revision history

Dirkjan at 19:51, 27 August 2020

2020-08-27T19:51:54Z

Dirkjan: Replaced content with "Unit Vector Category:math Category:Term"

2020-08-27T19:16:59Z

Replaced content with "Unit Vector Category:math Category:Term"

Dirkjan: Created page with "In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length). A unit vector is often denoted by a lowercase..."

2020-08-25T07:55:49Z

Created page with "In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length). A unit vector is often denoted by a lowercase..."

New page

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length). A unit vector is often denoted by a lowercase letter with a "hat", like this: i-hat (pronounced "i-hat").

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 <math>\hat{u}</math> of a non-zero vector u is the unit vector codirectional with u, i.e.,

<math>\hat{u}</math> = <math>\frac{u}{\|u\|}</math>

where vector u between two pairs of vertical lines is the norm (or length) of vector 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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+In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length). A unit vector is often denoted by a lowercase letter with a "hat", like this: i-hat (pronounced "i-hat").
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