Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Practice Exercises - Page 734: 42



Work Step by Step

Formula to calculate the angle between two plane vectors $a$ and $b$ is defined as: $ \theta = \cos ^{-1} (\dfrac{a \cdot b}{|a||b|})$ Here, $a=\lt 1,1,0 \gt$ and $b=\lt 0,1,1 \gt$ $|a|=\sqrt{1^2+1^2+0^2}= \sqrt {2}$ and $|b|=\sqrt{0^2+1^2+(1)^2}=\sqrt 2$ Thus, $ \theta = \cos ^{-1} (\dfrac{1}{ (\sqrt 2 )(\sqrt 2)})=\cos^{-1} (\dfrac{1}{2})=\dfrac{\pi}{3}$
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