Generally, only two planes are judged to be parallel, not intersecting. Of course, if two planes are not parallel, they must intersect.

The general rule for judging the parallelism of two planes is that two intersecting straight lines in one plane are parallel to two straight lines in another plane, or two planes perpendicular to the same straight line are parallel, but in either case, the overlap of two planes must be excluded.

These are all imaginary things, and the specific situation is analyzed.

If it is spatial analytic geometry, it can be judged by normal vector.