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 - Page 796: 9


$|PQ|=6$ $|QR|=2\sqrt{10}$ $|RP|=6$ The triangle is isosceles.

Work Step by Step

The side lengths can be calculated using the distance formula: $d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2)}$ $|PQ|=\sqrt{(7-3)^2+(0+2)^2+(1+3)^2)}=6$ $|QR|=\sqrt{(1-7)^2+(2-0)^2+(1-1)^2)}=\sqrt{40}=2\sqrt{10}$ $|RP|=\sqrt{(3-1)^2+(-2-2)^2+(-3-1)^2)}=6$ Since two of the legs are the same length, the triangle is isosceles.
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