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Mathematics-Online course: Vector Calculus - Planes

# Hesse-Form of a Plane

The position vector of a given point in a plane through point orthogonal to a normal vector satisfies

If and , then we obtain the so called Hessian normal form and is the distance between the plane and the origin.

Given a plane with unit normal vector throught point .

We have

i.e. the Hessian normal form of the plane ist given by

Then lies in this plane, because we have

On the other hand, does not lie in this plane, because we have