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: 16


$\textbf{r} = \langle 0,4,8\rangle + t\langle10,-9,-12 \rangle$

Work Step by Step

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$ $\textbf{r}_0 = \langle 0,4,8\rangle$ Given the two points, we can find $\textbf{v}$: $\textbf{v} = \langle10-0, -5-4, -4-8\rangle = \langle 10, -9, -12\rangle$ $\textbf{r} = \langle 0,4,8\rangle + t\langle10,-9,-12 \rangle$
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