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Vector equation of a plane

In three-dimensional Euclidean space, a plane may be characterized by a point contained in the plane and a vector that is perpendicular, or normal, to the plane.

The equation of the plane containing the point and perpendicular to the vector is

(The dot represents the dot product.)

Using the notation , , and , the expression becomes

or

.

(The vector is typically called the normal vector.)

Expanding and simplifying the expression, one obtains:

or

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