A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector 
having the same direction as a given (nonzero) vector 
is defined by
 |
where 
denotes the norm
of 
, is the unit vector in the same direction
as the (finite) vector 
. A unit vector in the 
direction is given by
 |
where 
is the radius
vector.
When considered as the 
th
basis vector of a vector
space, a unit vector may be written 
(or 
).
