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Mathematics · Glossary

What is Normal vector?

Definition 31.8 High School Mathematics · Chapter 31 — Vectors, Lines and Planes in Space

A normal vector of a plane P\mathcal P is a nonzero vector orthogonal to every vector lying in P\mathcal P (it suffices that it be orthogonal to two non-collinear directions of P\mathcal P).

A normal vector n of the plane P is orthogonal to every direction of P. The point H, foot of the perpendicular from M_0, realizes the distance from M_0 to the plane.
A normal vector n⃗\vec n of the plane P\mathcal P is orthogonal to every direction of P\mathcal P. The point HH, foot of the perpendicular from M0M_0, realizes the distance from M0M_0 to the plane.
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