Calculus: Early Transcendentals 8th Edition

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

Chapter 12 - Section 12.1 - Three-Dimensional Coordinate Systems - 12.1 Exercises: 11

Answer

11a. No 11b. Yes

Work Step by Step

Three points lie in a straight line (i.e. are collinear) if: $\frac{x_{1} -x_{2}}{x_{1} -x_{3}} = \frac{y_{1} -y_{2}}{y_{1} -y_{3}} = \frac{z_{1} -z_{2}}{z_{1} -z_{3}}$ a. $x: \frac{2-3}{2-1} = -1$ $y: \frac{4-7}{4-3} = -3$ $z: \frac{2+2}{2-3} = 4$ Clearly not collinear. b. $x: \frac{0-1}{0-3} = \frac{1}{3}$ $y: \frac{-5+2}{-5-4} = \frac{1}{3}$ $z: \frac{5-4}{5-2} = \frac{1}{3}$ Collinear
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