Table of Contents
Properties of Dot Products
The Prompt
“Write down something you know about the dot product.”
Context
This SWBQ is intended to be a quick review of the properties of the dot product.
Wrap Up
Collect a selection of responses from the students. Order them to make a coherent review and then hold them up and discuss the properties. Make sure to include an example of the geometric definition: $$\vec v \cdot \vec w = \vert \vec v \vert\; \vert \vec w\vert \cos\theta$$ and the algebraic definition: $$\vec v \cdot \vec w = v_x w_x + v_y w_y + v_z w_z$$ Also, tell the students that their power as a problem-solver comes from playing these two definitions off against each other. A good homework problem or small group activity, to emphasize this message, is for students to find the interior angle of a tetrahedron or the angle between a diagonal and a face-diagonal on a cube.
