forma normal de Hesse

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In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane R 2 {\displaystyle \mathbb {R} ^{2}} , a plane in Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} , or a hyperplane in higher dimensions. It is primarily used for calculating distances (see point-plane distance and point-line distance). It is written in vector notation as r → ⋅ n → 0 − d = 0. {\displaystyle {\vec {r}}\cdot {\vec {n}}_{0}-d=0.\,} The dot ⋅ {\displaystyle \cdot } indicates the dot product (or scalar product). Vector r → {\displaystyle {\vec {r}}} points from the origin of the coordinate system, O, to any point P that lies precisely in plane or on line E. The vector n → 0 {\displaystyle {\vec {n}}_{0}} represents the unit normal vector of plane or line E. The distance d ≥ 0 {\displaystyle d\geq 0} is the shortest distance from the origin O to the plane or line.