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.Unit Vector Formula

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.

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

$=\left(\frac{1}{15}\right)<9,12=””>$

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


Practise This Question

A ball is connected to a rope and swung around in uniform circular motion. The tension in the rope is measured at 10 N and the radius of the circle is 1 m. How much work is done in one revolution around the circle?