What is a normal vector to a circle plane?

I assume you mean the normal vector in the plane of the circle

If you write the circle in the form f(x,y,z) = 0 e.g. x^2 + y^2 - r^2 = 0


then grad(f) gives you the normal vector (outward pointing). In cartesian (x,y,z) coordinates:


grad(f) = (df/dx, df/dy, df/dz)




So in our example:


grad(f) = (2x, 2y, 0)


This is the normal vector and is necessarily in the plane of the circle, even if this method is followed for a circle with some angle to the x-y plane :)


This works for any function of the form f(...) = 0, not just circles...