## Calculus (3rd Edition)

$${\bf{r}}(t)= \langle -2+6t,3t,-2+9t \rangle.$$
To find a vector parametrization for the given line, we have to find the direction vector: $(4,3,7)-(-2,0,-2 )=\langle 6,3,9 \rangle$ Hence, we get the parametrization $${\bf{r}}(t)= \langle -2,0,-2 \rangle +t \langle 6,3,9 \rangle\\ = \langle -2+6t,3t,-2+9t \rangle.$$