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.
Three rectangular unit vectors
The three rectangular unit vectors
are illustrated in the figure.
Basically these unit vectors are 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.
Example
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.
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can be expressed in terms of its unit vector a in the following way
the magnitude of the vector
are illustrated in the figure.
where ax, ay
are the magnitudes of a along X, Y directions respectively.
