Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 685: 56



Work Step by Step

Since $ n_1=\langle 1,2,1\rangle $ and $ n_2=\langle 4,1,3\rangle $, then we have \begin{align*} \cos \theta &=\frac{n_1 \cdot n_2}{\|n_1\|\|n_2\|}\\ &=\frac{4+2+3}{\sqrt{1+4+1}\sqrt{16+1+9}}\\ &=\frac{9}{\sqrt{6}\sqrt{26}}. \end{align*} That is $$\theta=43.89^o.$$
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