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
.