Unit Vector

Unit Vector:

A unit vector is a vector that has a magnitude of exactly 1 unit and points in a particular direction.

A unit vector lacks both unit and dimension , But it have a magnitude of a unit and a certain direction. It’s sole purpose is to point toward a direction.

A unit vector is denoted by a letter above which a hat (  \hat{} ) is placed.


The unit vector along any vector ( say vector a ( \overrightarrow{a}) ) is calculated using the formula:

\hat{a} = \dfrac{\overrightarrow{a}}{| \overrightarrow{a} |}

Or by dividing the vector by it’s magnitude.

Unit Vector along x , y & z axes:


The unit vectors along x , y and z axis are denoted by \hat{i} , \hat{j} and \hat{k} respectively. as shown in the figure below:

unit vector

unit vector




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