If the normal vectors are parallel, the two planes are either identical or parallel. If the normal vectors are not parallel, then the two planes meet and make a line of intersection, which is the set of points that are on both planes.

To determine if two planes are the exact same physical aircraft, you must look at the tail number (registration number), which is a unique alphanumeric code painted on the rear fuselage or engines. This is the "legal name" of the aircraft and stays with it through different flights and call signs, though it can change if the plane is sold to an airline in a different country. For example, a U.S.-registered plane always starts with "N" (e.g., N904DE). You can Google this number to find the plane's age, owner, and maintenance history. If you only want to know if they are the same model, you can look for specific physical markers: the shape of the wingtips (winglets), the number and shape of the engines, the number of wheels on the landing gear, or the "nose" profile. For example, a Boeing 737 has a distinct pointed nose and flat-bottomed engine cowlings, while an Airbus A320 has a more rounded nose and circular engines. However, only the tail number provides 100% certainty of the aircraft's individual identity.