If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Unit: Vectors

Not feeling ready for this? Check out Get ready for Precalculus.

0

Possible mastery points

Vectors introduction

Learn
Intro to vectors and scalars
(Opens a modal)
Recognizing vectors
(Opens a modal)
Recognizing vectors practice
(Opens a modal)
Equivalent vectors
(Opens a modal)
Components of vectors
(Opens a modal)
Components of vectors (example 2)
(Opens a modal)
Practice
Equivalent vectorsGet 3 of 4 questions to level up!
Components of vectorsGet 3 of 4 questions to level up!

Magnitude of vectors

Learn
Vector magnitude from graph
(Opens a modal)
Vector magnitude from components
(Opens a modal)
Vector magnitude from initial & terminal points
(Opens a modal)
Practice
Magnitude of vectorsGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 300 Mastery points

Scalar multiplication

Learn
Scalar multiplication of vectors
(Opens a modal)
Analyzing scalar multiplication
(Opens a modal)
Practice
Scalar multiplicationGet 3 of 4 questions to level up!
Analyze scalar multiplicationGet 3 of 4 questions to level up!

Vector addition and subtraction

Learn
Adding & subtracting vectors
(Opens a modal)
Graphically adding & subtracting vectors
(Opens a modal)
Graphically subtracting vectors
(Opens a modal)
Adding vectors algebraically & graphically
(Opens a modal)
Practice
Add & subtract vectorsGet 3 of 4 questions to level up!
Graphically add & subtract vectorsGet 3 of 4 questions to level up!

Combined vector operations

Learn
Combined vector operations
(Opens a modal)
Vector operations review
(Opens a modal)
Practice
Combined vector operationsGet 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 500 Mastery points

Unit vectors

Learn
Unit vectors intro
(Opens a modal)
Worked example: finding unit vector with given direction
(Opens a modal)
Worked example: Scaling unit vectors
(Opens a modal)
Practice
Unit vectorsGet 3 of 4 questions to level up!

Magnitude and direction form of vectors

Learn
Direction of vectors from components: 1st & 2nd quadrants
(Opens a modal)
Direction of vectors from components: 3rd & 4th quadrants
(Opens a modal)
Vector forms review
(Opens a modal)
Practice
Direction of vectorsGet 3 of 4 questions to level up!

Component form of vectors

Learn
Vector components from magnitude & direction
(Opens a modal)
Vector components from magnitude & direction (advanced)
(Opens a modal)
Vector magnitude and direction review
(Opens a modal)
Practice
Vector components from magnitude & directionGet 3 of 4 questions to level up!

Adding vectors in magnitude and direction form

Learn
Adding vectors in magnitude & direction form (1 of 2)
(Opens a modal)
Adding vectors in magnitude & direction form (2 of 2)
(Opens a modal)
Vector addition & magnitude
(Opens a modal)
Practice
Add vectors: magnitude & direction to componentGet 3 of 4 questions to level up!
Add vectors: magnitude & directionGet 3 of 4 questions to level up!

Vectors word problems

Learn
Vectors word problem: pushing a box
(Opens a modal)
Vectors word problem: tug of war
(Opens a modal)
Vectors word problem: hiking
(Opens a modal)
Practice
Vector word problemsGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 600 Mastery points
Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 1400 Mastery points!

About this unit

Learn what vectors are and how they can be used to model real-world situations. Perform various operations with vectors like adding, subtracting, scaling, and conversion between rectangular to polar coordinates.