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Normal Vector

Alternate names

normal to a plane | principal normal vector | unit normal

Basic definition

A normal vector is a vector perpendicular to a surface.

Detailed definition

The normal vector, often simply called the "normal, " to a surface is a vector which is perpendicular to the surface at a given point. When normals are considered on closed surfaces, the inward-pointing normal (pointing towards the interior of the surface) and outward-pointing normal are usually distinguished. The unit vector obtained by normalizing the normal vector (i.e., dividing a nonzero normal vector by its vector norm) is the unit normal vector, often known simply as the "unit normal." Care should be taken to not confuse the terms "vector norm" (length of vector), "normal vector" (perpendicular vector) and "normalized vector" (unit-length vector).

Related terms

binormal vector | contact angle | curvature | Frenet formulas | multivariable calculus | norm | tangent vector | torsion

Educational grade level

high school level

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