Normalize (3, 4)T.
The vector is the hypotenuse of a 3-4-5 right triangle, so its length is 5. The unit vector is:
1/5 × (3,4)T = (3/5, 4/5)T = (0.6, 0.8)T
Scaling changes the length of a vector but not its direction. If vu is the unit vector corresponding to v, then vu and v have the same orientation.
This sounds plausible, but a demonstration might not hurt:
Start with v = (3, 4)T as above. Form vu = (3/5, 4/5)T. The direction of v is arc tan( 4/3 ). The direction of vu is arc tan( (4/5) / (3/5) ) = arc tan( (4/5) × (5/3) ) = arc tan( 4/3 )
Construct a unit vector in the same direction as w = (4, 6)T.