The dot product of two vectors is a way of "multiplying" two vectors; however, the result is not a vector, but a scalar. This scalar turns out to be very useful when you need to calculate various measurements, such as distances, lengths and angles.

In this learning object, we'll look at

  1. Two equivalent definitions of dot products,
  2. How to do calculations with dot products,
  3. Using dot products to calculate angles,
  4. Using dot products to find orthogonal projections.
Prerequisites. A basic knowledge of vectors and vector calculations.
Keywords: dot product, angle between vectors, orthogonal vectors, orthogonal projections