Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 13 - Vector Functions - Review - True-False Quiz - Page 897: 2



Work Step by Step

Given: $r(t)=(0,t^{2},4t)$ Here, $x=0,y=t^{2},z=4t$ As $z=4t$ gives $t=\frac{z}{4}$ and $y=t^{2}$ becomes $y=(\frac{z}{4})^{2}$ $y=\frac{z^{2}}{16}$ which represents a standard form of equation of a parabola in the $yz$ plane. Hence, the statement is true.
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