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: 59

Answer

$$\theta=55^o.$$

Work Step by Step

Since $ n_1=\langle 3,-5,2\rangle $ and $ n_2=\langle 1,0,1\rangle $, then we have \begin{align*} \cos \theta &=\frac{n_1 \cdot n_2}{\|n_1\|\|n_2\|}\\ &=\frac{3+0+2}{\sqrt{9+25+4}\sqrt{1+0+1}}\\ &=\frac{5}{\sqrt{38}\sqrt{2}}. \end{align*} Taking the inverse cosine of the above, we get:$$\theta=55^o.$$
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