Brown University Mathematics - Vector Boot Camp

prepared by Dan Katz

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.

Content Overview

Here are links to the three parts of the content overview:

If you don't feel like hearing my voice, 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

The worksheet of practice problems can be downloaded here.


The answers to the practice problems can be downloaded here.

In the future, I plan to add a video (or videos) showing how the practice problems are solved. For now, you can use the file above to check your answers, and if you run into difficulties, feel free to reach out to me.


You can reach me at dkatz [at] math [dot] brown [dot] edu.