## Calculus (3rd Edition)

$$r(t)=\langle 3+3t,-5,7+t\rangle.$$
The vector parametrization of the line is given by $$r(t)=(3,-5,7)+t\langle 3,0,1\rangle,$$ that is $$r(t)=\langle 3+3t,-5,7+t\rangle.$$