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:
Often this idea is written as a formula. The subscript "u" means "unit vector". Different books use different notation for this.
vu = v / |v|
If v = (x, y, z)T then:
vu = v / |v| = ( x /|v|, y/|v|, z/|v| )T
Normalize (3, 4)T.