Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.3 - Vectors in the Plane - 8.3 Exercises - Page 585: 14

Answer

Equivalent

Work Step by Step

NOTE: Two vectors are equivalent when they have the same magnitude and direction. To find the direction, we can use the slope. Slope of $\overrightarrow{u}$: $\frac{\Delta y}{\Delta x} = \frac{-1 -1}{13 - 8} = \frac{-2}{5} = -0.4$ Slope of $\overrightarrow{v}$: $\frac{\Delta y}{\Delta x} = \frac{6 - 4}{-7 - (-2)} = \frac{2}{-5} = -0.4$ Magnitude of $\overrightarrow{u}$: $\sqrt {(-2)^{2} + (5)^{2}} = 5.39$ Magnitude of $\overrightarrow{v}$: $\sqrt {(2)^{2} + (-5)^{2}} = 5.39$ Since the vectors have the same direction and magnitude, they are equivalent.
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