Editing Euclidean vector (section)

====Unit vector====
[[Image:Vector normalization.svg|class=skin-invert-image|thumb|right|The normalization of a vector '''a''' into a unit vector '''â''']]
{{main|Unit vector}}

A ''unit vector'' is any vector with a length of one; normally unit vectors are used simply to indicate direction. A vector of arbitrary length can be divided by its length to create a unit vector.<ref name="1.1: Vectors"/> This is known as ''normalizing'' a vector. A unit vector is often indicated with a hat as in '''â'''.

To normalize a vector {{nowrap|1='''a''' = (''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>)}}, scale the vector by the reciprocal of its length ‖'''a'''‖. That is:

<math display=block>\mathbf{\hat{a}} = \frac{\mathbf{a}}{\left\|\mathbf{a}\right\|} = \frac{a_1}{\left\|\mathbf{a}\right\|}\mathbf{e}_1 + \frac{a_2}{\left\|\mathbf{a}\right\|}\mathbf{e}_2 + \frac{a_3}{\left\|\mathbf{a}\right\|}\mathbf{e}_3</math>