Three Points Determine a Plane

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Three noncollinear points in three dimensions determine a unique plane with an equation of the form , where and is the positive distance of the plane from the origin. The vector is normal (perpendicular) to the plane and has norm (length) equal to 1.

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For such an equation, the signed distance from a point to the plane is given by . Points on the same side of the plane have the same sign.

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Contributed by: Ed Pegg Jr (December 2017)
Open content licensed under CC BY-NC-SA


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