Vector Algebra

brought to you by
taught by Steve Pomroy

In this course, you'll learn what vectors are and how to manipulate them.  After vectors are fully defined, we'll consider basic operations like addition and subtraction, and then move into the multiplication of vectors by the dot product and cross product.  By the time you've completed the course, you'll have a solid grounding in vector algebra, and you'll be ready to move on to the many applications throughout STEM disciplines.

The focus of the course is on physical vectors in 2- and 3-dimensional space.  We won't look a the more general mathematical vectors that might have any number of dimensions (up to infinity!).  This gives you a good foundation to work from if you want to continue into more advanced topics on vectors (including both higher dimensions and vector calculus).  It also gives you the tools you need to apply vectors to the study of the physical sciences.

What Will You Learn?

  • What are vectors? How are they different from scalars ("normal" numbers)?
  • What are the various ways to represent vectors?
  • How do you add, subtract, and scale vectors?
  • How do you convert between different representations of vectors?
  • What is a "dot product", and how do you calculate one?
  • What is a "cross product", and how do you calculate one?
  • What is a "triple product", and how do you calculate one?
  • What are some applications of vectors in STEM?

What Do You Need?

  • Comfort with algebra.
  • Comfort with trigonometry.
  • A prior introduction to vectors would be helpful, but is not necessary.

Who is This Course For?

  • Highschool students learning about or using vectors for the first time.
  • Early college or university STEM students learning about vectors and/or their applications.
  • Anyone interested in the mathematics of vectors.

Course Features

  • 17 Videos

    Over 4 hours of lecture materials and problem demonstrations

  • 7 Documents

    Practice Problems, some with solutions provided

  • 6 Quizzes

    Six opportunities to measure your progress

Course Content

  • 2

    Vector Basics

    • LECTURE: Definition and Description of Vectors

    • LECTURE: Basic Vector Operations

    • DEMO: Basic Vector Operations

    • PRACTICE: Basic Vector Operations

    • QUIZ: Vector Basics

  • 3

    Vector Conversions

    • LECTURE: Vector Conversions in 2 Dimensions

    • DEMO: Conversions in 2-D

    • PRACTICE: Conversions in 2-D

    • QUIZ: Vector Conversions in 2-D

    • LECTURE: Magnitudes and Angles in 3 Dimensions

    • DEMO: Magnitudes and Angles in 3-D

    • PRACTICE: Magnitude and Angles in 3-D

    • QUIZ: Magnitude and Angles in 3-D

  • 4

    The Dot Product

    • LECTURE: The Dot product (AKA - Scalar Product)

    • DEMO: The Dot Product

    • PRACTICE: The Dot Product

    • QUIZ: The Dot Product

  • 5

    The Cross Product

    • LECTURE: The Cross product (AKA - Vector Product)

    • DEMO: The Cross Product

    • PRACTICE: The Cross Product

    • LECTURE: Cross product Mnemonics

    • DEMO: Cross Product Mnemonics

    • PRACTICE: Cross product Mnemonics

    • QUIZ: The Cross product

  • 6

    The Triple Product

    • LECTURE: Triple Products of Vectors

    • DEMO: Triple Products

    • PRACTICE: Triple Products

    • QUIZ: Triple Products

  • 7

    Vectors Summary and Conclusion

Your Instructor

Steve Pomroy

Steve Pomroy holds an undergraduate degree in Mechanical Engineering and a Masters Degree in Aerospace Engineering.  With over 20 years in aviation and over 6,000 hours of flying time, most of Steve's professional experience is in flight operations.  Most recently, he's been operating as a Captain on a Dash-8-Q400 aircraft at a regional airline in Canada.

Steve's teaching background includes three years teaching Mechanical Engineering at an international college in the Middle East, and many years (and thousands of flight hours!) as a flight instructor, both civilian and military.  Aside from in-person instruction (both in the classroom and in the airplane), Steve has also worked behind-the-scenes on tutorial video development for  Currently, his program and course-development efforts are focused on engineering courses at

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