Answer
$$ x=3+3t, \quad y=-1+5t, \quad 1-7t.$$
Work Step by Step
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
$$ x=3+3t, \quad y=-1+5t, \quad 1-7t.$$
