Line perpendicular to an edge of a polyline on a plane in 3D

I have a plane (red) in 3D, and I have a curve (white) defined by vtkPolyLine which resides on the plane. The plane source is defined by vtkPlane and final plane data is computed by vtkCutter. I want to find a line (yellow) on the plane that is perpendicular to a particular edge of the curve. What is the fastest way to do this ?