Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 784: 88


Two vectors are said to be equal if they have same magnitude as well as same direction.

Work Step by Step

The magnitude of $\mathbf{u}$ is $\begin{align} & \left\| \mathbf{u} \right\|=\sqrt{{{\left( 1-0 \right)}^{2}}+{{\left( 2-0 \right)}^{2}}} \\ & =\sqrt{1+4} \\ & =\sqrt{5} \end{align}$ The magnitude of $\mathbf{v}$ is $\begin{align} & \left\| \mathbf{v} \right\|=\sqrt{{{\left( 3-2 \right)}^{2}}+{{\left( 2-0 \right)}^{2}}} \\ & =\sqrt{1+4} \\ & =\sqrt{5} \end{align}$ Both vectors have same magnitude and direction. Hence, $\mathbf{u}=\mathbf{v}$.
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