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Given a plane, one can introduce a Cartesian coordinate system on it in order to label every point on the plane uniquely with two numbers, its coordinates.
In a threedimensional xyz coordinate system, one can define a plane as the set of all solutions of an equation ax + by + cz + d = 0, where a, b, c and d are real numbers such that not all of a, b, c are zero. Alternatively, a plane may be described parametrically as the set of all points of the form u + s v + t w where s and t range over all real numbers, and u, v and w are given vectors defining the plane.
A plane is uniquely determined by any of the following combinations:
In threedimensional space, two different planes are either parallel or they intersect in a line. A line which is not parallel to a given plane intersects that plane in a single point.
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