Finding The Normal Plane At A Point To The Intersection Of Two Curves

If two curvesintersect, we can find the normal at a pointby looking at the gradients of the functionsand

is in the plane normal to f at the point (x_1 , y_1 , z_1 ) andis in the plane normal to g at the point (x_1 , y_1 , z_1 ) .

Henceis perpendicular to this plane.

For any vectorin the plane

This can be written