Unit Vector in Direction of Vector

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Let $\mathbf v$ be a vector quantity.

The unit vector $\mathbf {\hat v}$ in the direction of $\mathbf v$ is:

$\mathbf {\hat v} = \dfrac {\mathbf v} {\norm {\mathbf v} }$

where $\norm {\mathbf v}$ is the magnitude of $\mathbf v$.


From Vector Quantity as Scalar Product of Unit Vector Quantity:

$\mathbf v = \norm {\mathbf v} \mathbf {\hat v}$

whence the result.


Also presented as

This result is often seen presented as:

$\mathbf {\hat v} = \dfrac {\mathbf v} v$

as in this context $v$ is usually understood as being the magnitude of $\mathbf v$.