Planes

In geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions. It has no thickness and can be defined by a point and a normal vector, or by three non-collinear points. Any line contained in the plane lies entirely within it, and two planes either intersect in a line or are parallel (including the case of coincidence). In three-dimensional space, a plane is a two-dimensional affine subspace.

Planes, or airplanes, are powered, fixed-wing aircraft designed for transportation and other uses. They generate lift with wings as air moves over and under them, using propulsion to produce forward thrust. Planes are categorized by purpose, such as commercial airliners for passenger service, cargo planes, or military aircraft. A typical aircraft comprises a fuselage, wings, a tail assembly, landing gear, and control surfaces that manage pitch, roll, and yaw. Safe operation relies on aerodynamics, precise engineering, maintenance, and regulation, including air traffic control and certification. Environmental considerations include fuel efficiency and emissions, which drive ongoing advances in materials, engines, and design.