Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.1 Exercises - Page 876: 31

Answer

The points of view are (a) $(20,0,0)$ (b) $(-15,10,20)$ (c) $(20,15,25)$ (d) $(20,20,0)$

Work Step by Step

The point from which we look at the graph is determined by how the axes are oriented. (a) Here notice that we see $y$ and $z$ axis only, and the origin is in the center of our view. This means that we are sitting somewhere on the $x$ axis and the fact that the origin is centered implies that $y=0$ and $z=0$ so the point of view is $(20,0,0)$. (b) The $y$ and $z$ axes are directed towards us and the $x$ axis points away from us which says that $y$ and $z$ coordinates of our point of view are positive and the $x$ coordinate is negative so the point of view is $(-15,10,20)$. (c) All three axes point towards us so all three coordinates are positive so the point of view is $(20,15,25)$. (d) We see all three axes. $x$ and $y$ appear to be on the same line which is possible only if we are in the $xy$ plane where $z=0$. So our point of view is $(20,20,0)$.
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