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.

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