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: 41



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, $a=\lt 7,0,0 \gt$ and $b=\lt 1,1,\sqrt 2 \gt$ $|a|=\sqrt{7^2+0^2+0^2}= \sqrt {49}=7$ and $|b|=\sqrt{1^2+1^2+(\sqrt 2)^2}=2$ Hence, $ \theta =\cos ^{-1} (\dfrac{7}{ (7)(2)})=\dfrac{\pi}{3}$
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