Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.5 Lines and Curves in Space - 11.5 Exercises - Page 806: 11


$\textbf{r} = \langle 0,0,1\rangle + t\langle0,1,0 \rangle$

Work Step by Step

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$ $\textbf{r}_0 = \langle 0,0,1\rangle$ Since the line is parallel to the $y$-axis, the orientation of $\textbf{v}$ must be parallel to the $y$-axis. In other words, we can use the unit vector $\textbf{j}$ as our $\textbf{v}$. Thus, $\textbf{v} = \textbf{j}=\langle 0,1,0 \rangle $ $\textbf{r} = \langle 0,0,1\rangle + t\langle0,1,0 \rangle$
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