The normal plane to a curve at a point is defined as the plane containing the principal normal to the curve at the point and perpendicular to the tangent vector at the point.
To find the equation of the normal plane to the curve
at the point
(where
), take a point
in the plane then
is a vector in the tangent plane.
A tangent vector to the curve is given by
The normal plane is then given by
This simplifies to