## Calculus (3rd Edition)

$$x=3+3t, \quad y=-1+5t, \quad 1-7t.$$
The normal vector to the plane is $$n=\langle3,5,-7 \rangle$$ and it is easy to notice that the normal vector to the plane is the dirction vector of the line and hence the equation of the line is $$r(t)=\langle3,-1,1 \rangle+t\langle3,5,-7 \rangle.$$ Hence the parametric equations of the line are $$x=3+3t, \quad y=-1+5t, \quad 1-7t.$$