13. Planes in space





A plane can be described in many ways. The plane, for example, can be specified by three noncollinear points of the plane: there is a unique plane containing a given set of three noncollinear points in space. An alternative way to specify a plane is given as follows. Select a point P_{0} in the plane. There is a unique line through P_{0} perpendicular to the plane. This line is called the normal to to the plane at P_{0}. A vector n0 parallel to this normal is called a normal vector for the plane. There is a unique plane which passes through P_{0} and has n as a normal vector. Now P lies in the plane through P_{0} perpendicular to n if and only if and n are perpendicular. As = r  r_{0}, this condition is equivalent to
This is a vector equation of the plane.


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