Given a surface parameterized by the function [itex] f(x) [/itex] and a point p on that surface, assume that [itex] P [/itex] is a point on the tangent space of f at p. Find the normal vector to the hyperplane at [itex] P [/itex].
The Attempt at a Solution
The tangent hyperplane to f at p is given by the equation
[tex] \nabla f(p) \cdot ( x- p) = 0 [/tex]
Since we know that [itex] P [/itex] is on the tangent space, we must have that [itex] \nabla f(p) \cdot ( P - p ) = 0 [/itex]. However, here is where I am stuck. I'm not sure how to use this to calculate the normal vector. Any ideas?