Chapter 11 - Vectors and Vector-Valued Functions - 11.5 Lines and Curves in Space - 11.5 Exercises - Page 806: 25

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

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 $\textbf{v}$: $\textbf{v} = \langle1-0, 2-0, 3-0\rangle = \langle 1, 2, 3\rangle$ $\textbf{r} = \langle 0,0,0\rangle + t\langle1,2,3 \rangle = t\langle1,2,3 \rangle$