The Hesse normal form named after Otto Hesse, is an equation used in analytic geometry, and describes a line in or a plane in Euclidean space or a hyperplane in higher dimensions. It is primarily used for calculating distances, and is written in vector notation as
This equation is satisfied by all points P described by the location vector, which lie precisely in the plane E (or in 2D, on the line g).
The vector represents the unit normal vector of E or g, that points from the origin of the coordinate system to the plane (or line, in 2D). The distance is the distance from the origin to the plane (or line). The dot indicates the scalar product or dot product.
Read more about Hesse Normal Form: Derivation/Calculation From The Normal Form
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