Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.7 - The Dot Product - Concept and Vocabulary Check - Page 792: 3


If $\mathbf{v}\cdot \mathbf{w}=0$, then the vectors $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.

Work Step by Step

Dot product of two vectors is given as $\mathbf{v}\cdot \mathbf{w}=\left| \mathbf{v} \right|\left| \mathbf{w} \right|\cos \theta $ where $\theta $ is the angle between the vectors $\mathbf{v}$ and $\mathbf{w}$. The dot product between $\mathbf{v}$ and $\mathbf{w}$ is zero if the angle between them is $90{}^\circ $, which implies that the vectors are orthogonal to each other.
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