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I got the normal vectors, <1,1,1> and <1,0,1> and their cross product <1,0,-1> or i-k.

I set z to 0 and got x=0, y=1, z=0.

How do I form parametric equation out of this?? I know it's x=t, y=1, z=-t because this problem is nearly identical to one from lecture. But how did he do that step?

This would make the symmetric equations x/1=y-1/0=z/-1. But I can't divide by 0, can I?