Students will develop an understanding of the 3D dot product by building on their understanding of the 2D dot product. They will learn both definitions of the dot product, the first being component form, and the second being direction and magnitude form, also sometimes called the geometric definition of the dot product. For many ideas on how to give this lesson, watch this, this and this. Additionally, here's how you can prove the geometric definition of the dot product from an algebraic property of the dot product. Students should also learn and practice finding the dot product of two vectors. Before attempting this section, students should know the cosine law and understand the notation and concept for the magnitude of a vector.
Conclude by giving your students these challenges: