Plane through three points

Remark — Plane through three points

Given three non-collinear points $A,B,C$, a vector normal to the plane containing them is obtained with the vector product $\vec n = \vec{AB}\times\vec{AC};$ then one applies the point + normal formula using $A$ as base point.

The vector product of two sides of the triangle $ABC$ is perpendicular to both, hence to the plane containing them: it is exactly the normal vector sought.

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Topics: Analytic geometry in space
Concepts: Plane · Vector product · Normal vector
Skills: Analytic geometry · Using formulae