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Talk:PlanetPhysics/Dot Product

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%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: dot product %%% Primary Category Code: 02. %%% Filename: DotProduct.tex %%% Version: 3 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts}

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\begin{document}

The dot product or scalar product is defined as

$$ \mathbf{A} \cdot \mathbf{B} = A_x B_x + A_y B_y + A_z B_z $$

{\bf Geometric interpretation}

Using a geometric interpretation allows us to find the angle between two \htmladdnormallink{vectors}{http://planetphysics.us/encyclopedia/Vectors.html} because

$$ \mathbf{A} \cdot \mathbf{B} = \left | \mathbf{A} \right | \left | \mathbf{B} \right | \cos \theta$$

It is also useful to note that if the two vectors are perpindicular, their dot product is zero since


$$ \cos \left (90^o \right) = 0$$

\end{document}