Talk:PlanetPhysics/Dot Product
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[edit source]%%% 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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\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}