Mathematics-Online lexicon: Hesse Form of a Plane

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	Mathematics-Online lexicon:
	Hesse Form of a Plane

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The position vector $\vec{x}$ of a given point

in a plane through point

orthogonal to a normal vector $\vec{n}$ satisfies

$\displaystyle \vec{x}\cdot\vec{n} = d,\,\quad d=\vec{p}\cdot\vec{n}\, .$

If $\vert\vec{n}\vert=1$ and $d\ge0$ , then we obtain the so called Hessian normal form and

is the distance between the plane and the origin.

$\includegraphics[width=10cm]{hesse_form}$

Example:

automatically generated 3/28/2008