In geometry, a plane is an undefined term, meaning there is no definite description of what it is because it is so basic that it is the one used to define other terms in geometry. But we can still describe it as an area of any flat space. Now, you want plane M to intersect N but not O. Plane O also intersects N but not M. Therefore, the only way for planes M and O from not intersecting is if they are parallel planes. As drawn in the attached picture, planes N and M are the vertical side planes that have a particular distance. They may extend backwards are forwards, or upwards and downwards. But they will never meet. The other plane is drawn on the center with a slanting angle. It cuts through the two parallel planes.
