Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.5 - Equations of Lines and Planes - 12.5 Exercises - Page 832: 50

Answer

$cos \theta =\frac{6}{\sqrt {42}}$ or, $\theta =22.21 ^\circ$

Work Step by Step

Given: Planes $x+y+z=0$ and $x+2y+3z=1$ $n_1=\lt 1,1,1\gt$ and $n_2=\lt 1,2,3\gt$ To find the cosine of the angle, use formula: $cos \theta =\frac{n_1 \cdot n_2}{|n_1| |n_2|}$ $cos \theta =\dfrac{\lt 1,1,1\gt \cdot \lt 1,2,3\gt}{\sqrt {1^2+1^2+1^2}{\sqrt {1^2+2^2+3^2}}}$ $cos \theta =\frac{6}{\sqrt {42}}$ or, $\theta =22.21 ^\circ$
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