Does the following represent a unit vector: ( 1, 1, 1)T ?
No, its length is
( 12 + 12 + 12 ) = 4 = 2
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 little subscript "u" is supposed to mean "unit vector"):
vu = v / | v |
If v = (x, y, z)T then:
vu = v / | v | = ( x /| v |, y/| v |, z/ | v | )T