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%% 2. Change prswzzz everywhere (2x) to the basename of this file.
%% 3. Upload the PDF and PPT versions of the question.
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====== Properties of Dot Products ======

===== The Prompt =====

**"Write down something you know about the dot product."**

===== Context =====

This [[strategy:smallwhiteboard:|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.  

{{swbq:prsw:prswdot.ppt|Powerpoint slide}}
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{{swbq:prsw:prswdot.pdf|PDF slide}}



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