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: 40



Work Step by Step

We know that the angle between two vectors is: $\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$ Therefore, $||u||=\sqrt{6^2+3^2}=\sqrt{45}$ and $||v||=\sqrt{(-4)^2+(4)^2}= 4\sqrt {2}$ $\theta =\cos^{-1} [ \dfrac{(6)(-4)+(3)(4)}{ \sqrt{45} 4\sqrt {2}}]=\cos^{-1}[\dfrac{-12}{\sqrt{45}(4 \sqrt 2)}]$ So, $\theta =108.43^{\circ}$
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