Question

define unit vector.​

Answer 1

Answer:

unit vector is a vector that has a magnitude of 1 unit. A unit vector is also known as a direction vector. It is represented using a lowercase letter with a cap ('^') symbol along with it. A vector can be represented in space using unit vectors.

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Answer 2

Answer:

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 circumflex, or "hat", as in {\displaystyle {\hat {\mathbf {v} }}} {\hat {{\mathbf {v}}}} (pronounced "v-hat").[1][2]

The term direction vector is used to describe a unit vector being used to represent spatial direction, and such quantities are commonly denoted as d; 2D spatial directions represented this way are numerically equivalent to points on the unit circle. The same construct is used to specify spatial directions in 3D, which are equivalent to a point on the unit sphere.

Examples of two 2D direction vectors

Examples of two 3D direction vectors

The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,

{\displaystyle \mathbf {\hat {u}} ={\frac {\mathbf {u} }{|\mathbf {u} |}}} {\displaystyle \mathbf {\hat {u}} ={\frac {\mathbf {u} }{|\mathbf {u} |}}}

where |u| is the norm (or length) of u.[3][4] 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, and every vector in the space may be written as a linear combination of unit vectors.

By definition, the dot product of two unit vectors in a Euclidean space is a scalar value amounting to the cosine of the smaller subtended angle. In three-dimensional Euclidean space, the cross product of two arbitrary unit vectors is a third vector

Explanation:

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