Angle Inclination and Intersection of Two Surfaces

Angle of Inclination:
The angle between two planes is:

The angle of inclination is the angle between a given plane and the xy-plane. Because the vector k is normal to the xy-plane, we can use the above formula and plug in k. This is what we get: 

Intersection of Two Surfaces:

A line tangent to both of these surfaces is a line that lives on both tangent planes of the two surfaces. That is, it is the line of intersection of the two tangent planes.

Let's say we were given f(x,y,z) and g(x,y,z). To find, we cross product the two surface equations' gradients.