A plane is a two-dimensional surface that extends infinitely in all directions. In Euclidean geometry, a plane is defined by three points that are not in a straight line. Planes can be classified according to their orientation in space. The most common types of planes are the XY-plane (also called the ground or horizontal plane), which contains the x- and y-axes, and the XZ-plane (also called the vertical plane), which contains the x- and z-axes.
The angle between any two intersecting lines on a plane is called the angle of intersection. If two lines on a plane are perpendicular, then their angle of intersection is 90°. If two lines on a plane are parallel, then their angle of intersection is 0°.
A point on a plane can be specified using Cartesian coordinates (x,y) or polar coordinates (r,θ). The distance between any two points on a plane can be calculated using the Pythagorean theorem.
The equation of a straight line on a plane can be written in slope-intercept form: y=mx+b, where m is the slope of the line and b is the y-intercept. The equation of any other type of curve can also be expressed in Cartesian coordinates.
In physics and engineering, planes are often used as reference frames for measurements. For example, an aircraft’s altitude can be measured relative to sea level or to ground level; similarly, its velocity can be measured relative to the air around it or to ground level.