Solve both parts and justify the conditions used. Part A: State the intersection of two distinct planes known to share two distinct points. Part B: Similar solids have linear scale factor 3 from small to large. Find the surface-area ratio.

1. Part A reasoning

2. Use precise incidence conditions; diagrams alone do not prove spatial relationships.

3. Calculate or simplify this relation.

   $$A,B\in\alpha\cap\beta,\ A\ne B\Rightarrow AB\subseteq\alpha\cap\beta$$

4. Distinct intersecting planes meet in a line, not a finite segment.

5. Part B reasoning

6. Choose the correct surface or volume formula and keep units and similarity powers consistent.

7. Calculate or simplify this relation.

   $$S_{\text{large}}/S_{\text{small}}=3^2=9$$

8. The volume ratio would instead be 27.

A: The entire line through those two points. B: The requested value is 9.

Checks and common pitfalls: Distinct intersecting planes meet in a line, not a finite segment. The volume ratio would instead be 27.