A UNIT VECTOR is by definition a vector of Magnitude "one" (1) and no units of measurement associated to it.
If Á is a vector and A its magnitude, then the unit vector Â - pointing in the direction of Á - is given by:
They are useful when you need to give a scalar quantity a certain direction, but don't wish to change its value.
Unit vectors have magnitude 1 by definition but they can compose other vectors through vector algebra (head-to-tail summing). If you define vector Á
Á = 3î +6ĵ+ 4k^
Its magnitude is not one as A=sqrt(3²+6²+4²) and by definition it is not a unit vector.
What really are the unit vectors are the individual components i, j and k, which are scaled by 3, 6 and 4 respectively, giving the Á vector it's magnitude and direction.
The unit vectors i j and k point respectively towards the positive x, y and z directions and have magnitude 1. You can make a unit vector point in any direction though, using the formula I first stated.
You can easily identify unit vectors by the ^ (hat) notation.
Math Minor with Vector calculus
· 8 years ago