**Unit Vector Formula**

In mathematics, a unit vector in a normed vector space is a vector of length-1. A unit vector is often denoted by a lowercase letter with a “hat” $\widehat{i}$ . The term direction vector is used to describe a unit vector being used to represent spatial direction, and such quantities are commonly denoted as *d*.

Two 2D direction vectors, *d1* and *d2,* are illustrated. 2D spatial directions represented this way are equivalent numerically to points on the unit circle.

**Unit Vector Formula is given by**

\[\large \widehat{V}=\frac{v}{\left|v\right|}\]

Where,

*v* is magnitude of vector.

**Solved examples of Unit Vector **

**Example: **Find the direction of the vector v= <9, 12=>?

**Solution:**

Given,

v = <9, 12 =””>

Magnitude of the vector $\widehat{V}=\left|v\right|=\sqrt{9^{2}+12^{2}}=15$

Use the formula to find the magnitude of *v*.

$\widehat{V}=\frac{v}{\left|v\right|}$

$=\left(\frac{1}{15}\right)<9,12=””>$

$\left[\frac{3}{5},\frac{4}{5}\right]$

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