Vector Arithmetic

Interactive courseware module that addresses the fundamentals of vectors taught in mathematics courses.
Updated 10 Apr 2024

Vector Arithmetic

View on File Exchange or Open in MATLAB Online

MATLAB Versions Tested

Curriculum Module

Created with R2020b. Compatible with R2020b and later releases.


This curriculum module contains interactive MATLAB® live scripts that teach the fundamental concepts of vectors, such as vector magnitude and addition.


You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. VectorBasics is an interactive lesson that teaches the basics of individual vectors, such as vector components, vector magnitude, and vector orientation. VectorArithmetic is an interactive lesson that teaches vector arithmetic. Vector addition, scalar multiplication, dot product, and cross product are discussed. These methods are motivated by an application: calculating the orientation of a cell phone using the built-in accelerometer and magnetometer. Throughout the module, students apply the mathematical techniques to computing meaningful values, such as pitch and yaw.

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the EndIcon.png Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Contact Us

Solutions are available upon instructor request. Contact the MathWorks teaching resources team if you would like to request solutions, provide feedback, or if you have a question.


This module assumes knowledge of high school algebra and trigonometry. It does not assume any MATLAB knowledge. All scripts are intended to be used in Hidden Code mode.

Getting Started

Accessing the Module

On MATLAB Online:

Use the OpenInMO.png link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.

On Desktop:

Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double-click on VectorArithmetic.prj. It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start.

Ensure you have all the required products (listed below) installed. If you need to include a product, add it using the Add-On Explorer. To install an add-on, go to the Home tab and select AddOnsIcon.png Add-Ons > Get Add-Ons.


MATLAB® and Symbolic Math Toolbox™ are used throughout this module.


In this script, students will...
  • Relate the components of a vector to its visualization in 2- and 3-dimensions
  • Compute the magnitude of a vector in 2- and 3-dimensions
  • Compute the orientation of a vector in 2-dimensions
  • Discuss the meaning of the magnitude of an accelerometer reading
  • Relate the pitch of a cell phone to accelerometer readings
In this script, students will...
  • Add and subtract vectors
  • Compute scalar, dot, and cross products of vectors
  • Relate arithmetic vector operations to visual representations
  • Identify the physical meaning of the results of arithmetic vector operations
  • Apply vector arithmetic to compute the yaw of a cell phone


The license for this module is available in the

Related Courseware Modules

Courseware Module Sample Content Available on:
Matrix Methods of Linear Algebra image_5.png OpenInFX.png OpenInMO.png GitHub
Applied Linear Algebra image_8.png OpenInFX.png OpenInMO.png GitHub

Or feel free to explore our other modular courseware content.

Educator Resources


Looking for more? Find an issue? Have a suggestion? Please contact the MathWorks teaching resources team. If you want to contribute directly to this project, you can find information about how to do so in the page on GitHub.

© Copyright 2023 The MathWorks™, Inc

Cite As

Emma Smith Zbarsky (2024). Vector Arithmetic (, GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2020b
Compatible with R2020b and later releases
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes

See release notes for this release on GitHub:

See release notes for this release on GitHub:

See release notes for this release on GitHub:


To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.