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: 28


$\textbf{r} = \langle -1,-8,4\rangle + t\langle-8,13,-7 \rangle$

Work Step by Step

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$ Given points $(-1,-8,4)$ and $(-9,5,-3)$ Use one of the points as $\textbf{r}_0$ $\textbf{r}_0 = \langle -1,-8,4\rangle$ Given the two points, we can find $\textbf{v}$: $\textbf{v} = \langle-9+1, 5+8, -3-4\rangle = \langle -8,13,-7\rangle$ $\textbf{r} = \langle -1,-8,4\rangle + t\langle-8,13,-7 \rangle$
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