Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 854: 57


$109.5 ^\circ$

Work Step by Step

$a_1 \cdot a_2=|a_1||a_2| cos \theta$ $ \lt \frac{1}{2},-\frac{1}{2},-\frac{1}{2} \gt \cdot \lt -\frac{1}{2},\frac{1}{2},-\frac{1}{2} \gt=\sqrt {(\frac{1}{2})^2+(-\frac{1}{2})^2+(-\frac{1}{2})^2}\sqrt {(-\frac{1}{2})^2+(\frac{1}{2})^2+(-\frac{1}{2})^2} cos \theta$ $-\frac{1}{4}-\frac{1}{4}+\frac{1}{4}=\frac{3}{4} cos \theta$ $cos \theta =-\frac{1}{3}$ $ \theta = arccos (-\frac{1}{3})\approx 109.5 ^\circ$
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