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Mathematics-Online course: Vector Calculus - Planes

# Distance Point - Plane

Given a plane with normal vector through point . Let be the perpendicular projection of a given point onto this plane. The so called perpendicular vector of point onto the plane is given by

Its length

is the distance of the plane from .

The scalar product

yields the -fold distance between and the plane, where the sign indicates whether lies on the same side of the plane as does.

Thus we have

und

Given the plane with normal vector through point . We want to compute the distance of point from the plane and the foot of the perpendicular through this point onto the plane.

First of all we have

So we obtain

and finally we compute