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 **v _{u}** is the unit vector corresponding to

This sounds plausible, but a demonstration might not hurt:

Start withv= (3, 4)^{T}as above. Formv= (3/5, 4/5)_{u}^{T}. The direction ofvis arc tan( 4/3 ). The direction ofvis arc tan( (4/5) / (3/5) ) = arc tan( (4/5) × (5/3) ) = arc tan( 4/3 )_{u}

Construct a unit vector in the same direction as **w** = (4, 6)^{T}.