It is a vector having unit magnitude. It is used to denote the direction of a given vector.
Any vector can be expressed in terms of its unit vector a in the following way the magnitude of the vector
Therefore, if a given vector is divided by its magnitude, we get a unit vector.
The three rectangular unit vectors are illustrated in the figure.
Basically these unit vectorsare used to specify the positive X, Y, Z directions respectively.
Note that
need not be located at the origin. Like all vectors, they can be translated anywhere in the coordinate space, as long as their directions with respect to the coordinate axes are not changed.
The vector , as shown in the figure, is expressed in terms of its components and unit vectors as, where ax, ay are the magnitudes of a along X, Y directions respectively.
