Does the following represent a unit vector: ( 1, 1, 1)T ?

A good answer might be:

No, its length is 

( 12 + 12 + 12 ) =  4 =  2

Creating Unit Vectors

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:

  1. Calculate the length of v,   | v |.
  2. Scale v by the inverse of its length:   v / | v |

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

QUESTION 10:

Normalize (3, 4)T.