= Unit Vector =

A '''unit vector''' is a normalized vector, that is to say it has a [[Calculus/Distance|distance]] of 1.

<<TableOfContents>>

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== Description ==

A unit vector is a vector with a [[Calculus/Distance|distance]] of 1. Any vector can be made into a unit vector, by normalizing it: ''a⃗/||a⃗||''.

''R^3^'' space is commonly expressed as having the unit basis vectors ''î'', ''ĵ'', and ''k̂'' in the directions of the X, Y, and Z axes respectively.

Note that the [[Calculus/VectorOperations#Dot_Product|dot products]] of these unit vectors are characterized by:
 * ''i⋅i = j⋅j = k⋅k = 1''
 * ''i⋅j = j⋅k = k⋅i = 0''

Note also that the [[Calculus/VectorOperations#Cross_Product|cross products]] of these unit vectors are characterized by:
 * ''i×i = j×j = k×k = 0''
 * ''i×j = k''
 * ''j×k = i''
 * ''k×i = j''
 * ''j×i = -k''
 * ''k×j = -i''
 * ''i×k = -j''



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CategoryRicottone