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Inner product, Dot product

The inner product, or dot product, of two vectors $\QTR{bf}{u}$ and $\QTR{bf}{v}$ is defined asMATHwhere $\theta $ is the angle between $\QTR{bf}{u}$ and $\QTR{bf}{v}$, and MATH and MATH are the lengths of the vectors $\QTR{bf}{u}$ and $\QTR{bf}{v}$, respectively.

The inner product or dot product of two vectors in $\QTR{Bbb}{R}^{2}$ is given algebraically byMATH

The inner product or dot product of two vectors in $\QTR{Bbb}{R}^{3}$ is given algebraically byMATH

The inner product is a number, not a vector. If $\QTR{bf}{u}$ and $\QTR{bf}{v}$ are perpendicular, then MATH.


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Cross product


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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