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| ''R^3^'' space is commonly expressed as having the unit vectors ''î'', ''ĵ'', and ''k̂'' which each have a [[Calculus/Distance|distance]] of 1 in the directions of the X, Y, and Z axes respectively. | 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'' |
Unit Vector
A unit vector is a normalized vector, that is to say it has a distance of 1.
Contents
Description
A unit vector is a vector with a distance of 1. Any vector can be made into a unit vector, by normalizing it: a⃗/||a⃗||.
R3 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 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 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