Finding the Equation of the Rectifying Plane to a Curve at a Point

The rectifying plane at a point on a curve is the plane containing the tangent vector and the binormal vector to the curve at that point, so the plane is perpendicular to the principal normal.

To find the equation of the rectifying plane to the curveat the point(where), take a pointin the plane thenis a vector in the rectifying plane.

A tangent vector to the curve is given by

so at

Sinceandis normal ,

Hence

Hence

This simplifies to