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: 32



Work Step by Step

We know that the angle between two vectors is: $\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$ Therefore, $||u||=\sqrt{2^2+(-3)^2}=\sqrt{13}$ and $||v||=\sqrt{1^2+(-2)^2}=\sqrt 5$ $\theta =\cos^{-1} [ \dfrac{(2)(1)+(-3)(-2)}{ \sqrt {13}\sqrt 5}]=\cos^{-1}[\dfrac{8}{\sqrt 5 \sqrt{13}}]$ So, $\theta =7.13^{\circ}$
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