Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - Review - Exercises - Page 883: 24


(a) Neither parallel nor perpendicular (b) $57.584^\circ\approx 58^\circ$ (correct to nearest degree) (correct to nearest degree)

Work Step by Step

(a) From the equations, the coefficients of $x,y,z$ are the components of the normal vectors to the planes. $ \lt 1,1,-1\gt \cdot \lt 2,-3,4 \gt 1(2)+1(-3)+(-1)(4)$ $$=-5$$ They are neither perpendicular or orthogonal because their dot product is not zero nor parallel they are not multiples of each other. (b) $ \cos \theta =\frac{-5}{\sqrt 3 \sqrt {29}}$ $ \theta=\frac{-5}{\sqrt {87}}\approx 122.4 ^\circ$ The acute angle between the planes: $180^\circ-122.4 ^\circ=57.584^\circ\approx 58^\circ$ (correct to nearest degree) (correct to nearest degree)
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