It is easy to know that plane π passes through (1, 1, 1), (0,0) and (1, 0).

Three points of a line do not define a plane, and let the plane equation be ax+by+cz=0.

In addition, a+b+c=0, a=0,

Furthermore, b=-c≠0,

The plane equation is by-bz=0, which is simplified to y-z=0.

So the plane equation is y-z=0.