Department of Mathematics

Vector Boot Camp

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Vector Boot Camp

The resources on this page are intended to help students learn and/or review the basics of vectors and vector algebra for use in Brown University STEM courses. This "boot camp" module consists of a content overview, a set of practice problems, and solutions to those problems (currently just the final answers, although step-by-step video solutions may be added later).

You can use these in any way you find useful, but attempting to solve the problems is much more likely to help you than passively watching the review and solutions.

The video review is split into three parts. The first part covers vectors and scalars and explains how to add, subtract, and scale vectors in two and three dimensions. The second part covers the dot product in two and three dimensions, along with some basic applications. The third part covers the cross product in three dimensions. The practice problems are not split into parts, since part of the challenge of solving some of them is deciding what methods to use.

Vector Boot Camp - Content Overview

https://www.youtube.com/embed/lTvelzDUamo

Part 1

 

Vectors and Scalars

https://www.youtube.com/embed/zl-FpvGIJRU

Part 2

 

The Dot Product

https://www.youtube.com/embed/yfzxF7-5jUY

Part 3

 

The Cross Product

Slides from the Videos

You can also look at the slides used to produce the video, in PDF form. However, be aware that some of the pictures in the PDFs are incomplete (details are added live during the video) and many points are clarified and/or elaborated on in the video. So if you only look at the slides, you'll be missing some content.

Practice Exercises

Download the worksheet of practice problems

Solutions

In the future, video(s) will be added showing how the practice problems are solved. For now, you can use the file to check your answers, and if you run into difficulties, feel free to reach out with questions.

Download the answers to the practice problems

Questions