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: 14



Work Step by Step

Since, $(t,t,t)$ and $(t^{3},t^{3},t^{3})$ refers to same line but at the value of $t=1$ all they would have different tangent vectors such as $(1,1,1)$ and $(3,3,3)$. This implies that they would have same directions but different magnitudes. Hence, the given statement is false.
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