Final answer:
Many of the statements provided cannot be definitively answered without additional information. To accurately determine relationships such as parallelism, skewness, and coplanarity, more context about the points and lines in question is needed.
Step-by-step explanation:
Given that TK is parallel to ZM, we can examine the provided statements individually:
- A: It is not possible to determine whether K and I do not lie in the same plane without additional information about I.
- B: K and I are skew if they are not coplanar and do not intersect. This cannot be determined without more information about I.
- C: There is insufficient information provided to conclude whether TK and I are perpendicular.
- D: K and IM may lie in the same plane if IM existence intersects TK or is parallel to it, but we cannot confirm this without more details about I and M.
- E: K and M are not parallel unless KM is a line segment or vector that can be directly compared to TK, which is not established by the information provided.
- F: We cannot establish whether K and I do not intersect without more information.
Without additional context about the lines or points mentioned, many of these statements cannot be definitively answered. We need more specific geometric or vector relations between these elements.