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 - 13.4 Exercises - Page 894: 10

Answer

$\lt -2 \sin t,3, 2 \cos t\gt$, $\lt -2 \cos t, 0, -2 \sin t\gt$ , $\sqrt {13}$

Work Step by Step

Given: $r(t)=\lt 2 \cos t,3t, 2 \sin t \gt$ Our aim is to calculate the velocity vector, acceleration vector and speed. In order to calculate the all above terms we will use formulas, such as: $v(t)=r'(t)$ and $a(t)=v'(t)$ and speed is the magnitude of the velocity vector, that is $s(t)=|v(t)|$. Now, $v(t)=r'(t)=\lt -2 \sin t,3, 2 \cos t\gt$ $a(t)=v'(t)=\lt -2 \cos t, 0, -2 \sin t\gt$ $s(t)=|v(t)|=\sqrt {(-2 \sin t)^2+(3)^2+(2 \cos t)^2}=\sqrt {13}$ Hence, the required answers are: $\lt -2 \sin t,3, 2 \cos t\gt$, $\lt -2 \cos t, 0, -2 \sin t\gt$ , $\sqrt {13}$
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