Planes and Contours — Contact Possibilities Is the claim that a plane surface cannot intersect or be tangent to a contoured surface accurate, or can a plane both intersect and be tangent depending on geometry and positioning?

Introduction / Context:
Design and inspection often use planes to evaluate or generate features on complex contoured surfaces. The assertion that a plane surface cannot intersect or be tangent to a contoured surface is contrary to basic geometry. This question checks the understanding that a plane can have several relationships with a curved or contoured surface, including intersection along a curve and tangency at a single line or point depending on the specific shape.

Given Data / Assumptions:

• Contoured surfaces include cylinders, cones, spheres, and freeform profiles.
• A plane can be oriented arbitrarily in space relative to the part.
• Standard projection rules apply for representing the resulting line or contact region.

Concept / Approach:
When a plane intersects a curved surface, the set of all points common to both is a curve, for example an ellipse on a cylinder or a circle on a sphere under special conditions. When a plane is exactly tangent, the surfaces meet without cutting, sharing a common tangent direction at the contact locus, and no sharp edge line is drawn in orthographic views. Therefore the absolute negative claim in the stem is incorrect.

Step-by-Step Solution:
1) Visualize relative orientation between the plane and the curved surface.2) For most orientations, the plane cuts the surface producing a true intersection curve.3) For the special tangent orientation, the plane just touches with matched slope and forms no sharp edge.4) Represent intersection with visible or hidden edges; represent tangency with smooth contour only.

Verification / Alternative check:
Classic examples include slicing a cylinder or sphere with a plane. CAD section tools show the resulting curves and confirm basic geometric relationships.

Why Other Options Are Wrong:
Correct repeats the false statement. Only tangent but not intersect and Only intersect but not tangent impose artificial limits. Context-dependent is unnecessary because the general geometric possibilities are known.

Common Pitfalls:
Drawing an edge at a tangent contact; misidentifying section curves due to projection distortion in non principal views.

Final Answer:
Incorrect