# Unit vector

### Unit vector

In this section, we will learn what is a unit vector, which literally refers to a vector with magnitude of 1 unit. We will practice on calculating a unit vector as well as exploring how this concept relates to the basic unit vectors that are found in vectors represented in rectangular form.

#### Lessons

Unit Vector = a vector with a magnitude of 1
Given vector $\vec{v}$, the unit vector in the direction of vector $\vec{v}$ is obtained as follows:

$\hat{u}=\frac{\vec{v}}{||\vec{v}||}$
where $||\hat{u}||=1$
• Introduction
Introduction to Unit Vectors

• 1.
Find the unit vector of $\vec{a}=$<$6,-8$>, and verify

• 2.
What is a unit vector which has the same direction as $\vec{b}=3i+4j$?

• 3.
Given $\vec{v}=$<$10,-3$> and $\vec{w}=$<$-6,8$>,
a)
find $\vec{v}+\vec{w}$

b)
find the unit vector of the resultant vector

• 4.
Given $\vec{v}=$<$-5,6$> and $\vec{w}=$<$7,4$>,
a)
find $\vec{v}-\vec{w}$

b)
find the unit vector of the resultant vector