The plane spanned by the three points , , and on a curve as . Let be a point on the osculating plane, then

where denotes the scalar triple product. The osculating plane passes through the tangent. The intersection of the osculating plane with the normal plane is known as the principal normal vector. The vectors and (tangent vector and normal vector) span the osculating plane.

CITE THIS AS:

Weisstein, Eric W. "Osculating Plane." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/OsculatingPlane.html