Question
Horizontal plane Q and vertical plane R intersect at a line. Lines d and c are vertical and parallel to each other on plane R. Line B is horizontal on plane Q. Line a is diagonal on plane Q.
Marissa says that lines a and d will eventually intersect. Is she correct? Explain.
yes, because they are on the same plane
yes, because they are perpendicular
no, because they are parallel
no, because they are skew
Answers
GPT-4o mini
To determine whether lines a and d will eventually intersect, we need to analyze their orientations based on the information provided.
1. **Line a**: This line is diagonal on the horizontal plane (Q).
2. **Line d**: This is a vertical line on the vertical plane (R).
Since line a is on the horizontal plane and line d is on the vertical plane, they don't lie in the same plane. Moreover, they neither intersect nor are parallel.
Lines are considered **skew** if they do not intersect and are not parallel, which is the case here as one line is in a horizontal plane while the other is in a vertical plane.
Therefore, the correct answer is:
**no, because they are skew.**
1. **Line a**: This line is diagonal on the horizontal plane (Q).
2. **Line d**: This is a vertical line on the vertical plane (R).
Since line a is on the horizontal plane and line d is on the vertical plane, they don't lie in the same plane. Moreover, they neither intersect nor are parallel.
Lines are considered **skew** if they do not intersect and are not parallel, which is the case here as one line is in a horizontal plane while the other is in a vertical plane.
Therefore, the correct answer is:
**no, because they are skew.**