A sphere of radius 7 has its center at (10, 10, 10). The point, (12, 13, 16), lies on the sphere. A unique light sources is located at (100, 100, 100).

a. Find the unit normal to the sphere at the point (12, 13, 16).

b. Find the unit vector in the direction from the point (12, 13, 16) to a light source at (100, 100, 100).

c. What is the factor for diffuse shading at the point (12, 13, 16)? Show the actual numbers used in the calculation. You do not have to complete the arithmetic.