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: 53

Answer

$135^{\circ}$

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: $\overrightarrow{a} \cdot \overrightarrow{ b}= (2)(-3) +(1) (1) =-5$ and $|a|=\sqrt {2^1+1^1}=\sqrt 5; |b|=\sqrt {(-3)^1+1^1}=\sqrt {10}$ Therefore, $ \theta =\cos^{-1} (\dfrac{-5 }{\sqrt 5 \sqrt {10}})=135^{\circ}$
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