Does the following represent a unit vector: (1, 1, 1)T ?
No, its length
√( 12 + 12 + 12 ) = √3 = 1.7320508
is not one.
Unit vectors have a length of one. If you have a particular vector v you can use it to make a unit vector. This is called normalizing the vector:
Calculate the length of v, | v |. Scale v by dividing by its length: v / | v |
Often this idea is written as a formula. The subscript "u" means "unit vector".
vu = v / |v|
If v = (x, y, z)T then:
vu = v / |v| = ( x /|v|, y/|v|, z/|v| )T
Different books use different notation for this. Sometimes a "hat" is used for unit vectors: î but this does not show up well in browsers. Sometimes a unit vector is called a "normalized" vector.
Normalize (3, 4)T.