Let C be the curve of intersection of the spheres x² + y² + z² = 3 and (x − 2)² + (y − 2)² + z² = 3. Use the result of Exercise 63 to find parametric equations of the tangent line to C at P = (1, 1, 1).

Data From Exercise  63

Suppose that the intersection of two surfaces F(x, y, z) = 0 and G(x, y, z) = 0 is a curve C, and let P be a point on C. Explain why the vector v = ∇F_P × ∇G_P is a direction vector for the tangent line to C at P.