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: 25


$\textbf{r} = t\langle1,2,3 \rangle$

Work Step by Step

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$ Given points $(0,0,0)$ and $(1,2,3)$ Use one of the points as $\textbf{r}_0$ $\textbf{r}_0 = \langle 0,0,0\rangle$ Given the two points, we can find $\textbf{v}$: $\textbf{v} = \langle1-0, 2-0, 3-0\rangle = \langle 1, 2, 3\rangle$ $\textbf{r} = \langle 0,0,0\rangle + t\langle1,2,3 \rangle = t\langle1,2,3 \rangle$
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