WOLFRAM|DEMONSTRATIONS PROJECT

Normalizing Vectors

vectors

dimension

2

3

new set of vectors

A nonzero vector is normalized by dividing it by its length. The resulting vector has length 1 and lies in the same direction.

In 2D, the length of

v=(x,y)

is given by Pythagoras's formula:

|v|=

2

x

+

2

y

.

In 3D, the length of

v=(x,y,z)

is

|v|=

2

x

+

2

y

+

2

z

.

In any dimension, the normalized vector of

v

is

v/|v|=v

v·v

.