If RM, which of the following statements are true?
Check all that apply.
A.and do not intersect.
B. and lie in the same plane.
C. and do not lie in the same plane.
D. and are parallel.
and are perpendicular.
F. and are skew.



Answer :

Answer:If \( \mathbb{R}^3 \) refers to the three-dimensional Euclidean space, the relationships between lines can be described as follows:

1. **Two lines that do not intersect**:

  - They can either be parallel or skew.

2. **Two lines lying in the same plane**:

  - They can either intersect or be parallel.

3. **Two lines not lying in the same plane**:

  - They are skew.

4. **Two lines that are parallel**:

  - They lie in the same plane and do not intersect.

5. **Two lines that are perpendicular**:

  - They intersect and form a right angle.

6. **Two lines that are skew**:

  - They do not intersect and do not lie in the same plane.

Based on this, the correctness of each statement can be assessed:

- A. and do not intersect: This can be true if the lines are either parallel or skew.

- B. and lie in the same plane: This can be true if the lines either intersect or are parallel.

- C. and do not lie in the same plane: This is true if the lines are skew.

- D. and are parallel: This implies the lines do not intersect and lie in the same plane.

- E. and are perpendicular: This implies the lines intersect at a right angle.

- F. and are skew: This implies the lines do not intersect and do not lie in the same plane.

Therefore:

- Statements A, B, C, and D can be true in certain contexts.

- Statement E is true if the lines intersect at a right angle.

- Statement F is true if the lines do not intersect and do not lie in the same plane.

Step-by-step explanation: