I want to find parametric and symmetric equations for the line of intersection of the planes $x+y+z=1$ and $x+z$=0. Here's what I have so far:
I need to find a point on this line of intersection. So by setting z=0 in the equation of both planes, I get $x=0, y=1, z=0$. So $(0,1,0)$ is on the line. Now since this line is intersecting both planes, it must be perpendicular to both planes. So to find a line parallel to this line, I take the cross product of the normal vectors of both planes. I get $<1,-1,0>$. And now I'm stuck. I dont know what to do next. Any ideas?