Section 14.6: Directional Derivatives & Gradient Vector

Where does the helix \(\mathbf{r}(t) = \langle \cos(\pi t), \sin(\pi t), t \rangle\) intersect the paraboloid \(z = x^2 + y^2\)? What is the angle of intersection between the helix and the paraboloid? (This is the angle between the tangent vector to the curve and the tangent plane to the paraboloid.)