Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.4 Algebraically Defined Vectors and the Dot Product - 8.4 Exercises - Page 790: 56

Answer

$45^{\circ}$

Work Step by Step

To obtain the angle $\theta$ between two non-zero vectors $a$ and $b$, we will use the following formula such as: $ \theta =\cos^{-1} (\dfrac{\overrightarrow{a} \cdot \overrightarrow{ b} }{|a| |b|})$ We have: $\overrightarrow{a} \cdot \overrightarrow{ b}= (4)(2) +(0) (2) =8$ and $|a|=\sqrt {(4)^2+(0)^2}=4 ; |b|=\sqrt {(2)^2+(2)^2}=\sqrt { 8}$ Therefore, $ \theta =\cos^{-1} (\dfrac{8}{4\sqrt 8})= 45^{\circ}$
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