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 curve
at the point
(where
), take a point
in the plane then
is a vector in the rectifying plane.
A tangent vector to the curve is given by
so at
Since
and
is normal ,
Hence
Hence
This simplifies to
