Chapter 11 - Vectors and Vector-Valued Functions - 11.5 Lines and Curves in Space - 11.5 Exercises - Page 806: 27

$\textbf{r} = \langle 2,4,8\rangle + t\langle5,1,-5 \rangle$

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$ Given points $(2,4,8)$ and $(7,5,3)$ Use one of the points as $\textbf{r}_0$ $\textbf{r}_0 = \langle 2,4,8\rangle$ Given the two points, we can find $\textbf{v}$: $\textbf{v} = \langle7-2, 5-4, 3-8\rangle = \langle 5,1,-5\rangle$ $\textbf{r} = \langle 2,4,8\rangle + t\langle5,1,-5 \rangle$