Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 12 - Vector-Valued Functions - 12.1 Introduction To Vector-Valued Functions - Exercises Set 12.1 - Page 846: 6

Answer

$ \mathbf{r}(t) = 2t\mathbf{i} + 2\sin(3t)\mathbf{j} + 5\cos(3t)\mathbf{k}$

Work Step by Step

Step 1 Given: \[ x = 2t, \quad y = 2\sin(3t), \quad z = 5\cos(3t) \] Step 2 Then the vector equation of the curve given by: \[ \mathbf{r}(t) = x(t)\mathbf{i} + y(t)\mathbf{j} + z(t)\mathbf{k} \] is: \[ \mathbf{r}(t) = 2t\mathbf{i} + (2\sin(3t))\mathbf{j} + (5\cos(3t))\mathbf{k} \] Result \[ \mathbf{r}(t) = 2t\mathbf{i} + 2\sin(3t)\mathbf{j} + 5\cos(3t)\mathbf{k} \]
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