Which of the following statements about normal sections is true?

• A. They are defined by a plane that contains the normal at A and passes through B
• B. They lie in the tangent plane at A
• C. They are always parallel to AB
• D. All the above

Answer: (D)

Normal sections are curves obtained by cutting the surface with a plane that contains the surface normal at the point and a chosen direction in the tangent plane at that point. Here, the plane is defined by the normal at A and the line AB in the tangent plane. Since AB passes through both A and B, the plane through AB and the normal at A also passes through B. The intersection of this plane with the surface gives the normal section, and at A its tangent direction is along AB, so the section is parallel to AB. Because AB lies in the tangent plane, the initial direction of the normal section sits in the tangent plane as well. In this way, all the stated aspects align with how a normal section is constructed and behaves.