Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.1 - Three-Dimensional Coordinate Systems - Exercises 12.1 - Page 696: 44



Work Step by Step

Formula to find the distance between two points is $|PQ|=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$ Let us consider $P=(3,4,5)$ and $Q=(2,3,4)$ Now, $|PQ|=\sqrt{(2-3)^2+(3-4)^2+(4-5)^2}=\sqrt{(-1)^2+(-1)^2+(1)^2}$ or, $|PQ|=\sqrt {1+1+1}=\sqrt{3}$
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