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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 $ X$ in a plane through point $ P$ 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 $ d$ is the distance between the plane and the origin.

\includegraphics[width=10cm]{hesse_form}

see also:

[Examples]
  automatically generated 3/28/2008