Chapter 12: Vectors and the Geometry of Space - Section 12.5 - Lines and Planes in Space - Exercises 12.5 - Page 727: 57

$x=1-t; y=1+t; z=-1$

We are given that the equation of plane is: $1+y+z=1 ; 1+y=2$ Since, $r=r_0+tv$ and $v=\lt -1,1,0 \gt$ Now, let us consider $x=1$ and $y=1$ and $z=0-y=0-1=-1$ Thus, $r_0=\lt 1,1,-1 \gt$ The parametric equations are $x=1-t; y=1+t; z=-1+(0)t=-1$ or, $x=1-t; y=1+t; z=-1$