Algebra and Trigonometry 10th Edition

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

Chapter 8 - 8.4 - Vectors and Dot Products - 8.4 Exercises - Page 595: 39



Work Step by Step

We know that the angle between two vectors is: $\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$ Therefore, $||u||=\sqrt{3^2+4^2}=5$ and $||v||=\sqrt{(-7)^2+(5)^2}=\sqrt {74}$ $\theta =\cos^{-1} [ \dfrac{(3)(-7)+(4)(5)}{ 4\sqrt {13}}]=\cos^{-1}[\dfrac{-1}{5\sqrt{74}}]$ So, $\theta =91.33^{\circ}$
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