Unit vector

Intro Lesson
12:16
Lesson: 1
4:33
Lesson: 2
8:25
Lesson: 3
5:25
Lesson: 4
5:31

Learn

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.

Basic Concepts: Pythagorean theorem, Converting radicals to mixed radicals, Rationalize the denominator

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

Unit vector

Unit vector

Lessons

Do better in math today