To understand the relationship between the lines in the diagram, we need to analyze their orientations and the planes they lie on.

• Plane A is horizontal, and Plane B is vertical.
• Line n is vertical and lies on Plane B.
• Line m is horizontal and lies on Plane A.
• Line l is diagonal on Plane A.

Let's examine the relationships between the lines:

1. l and m:
   Both l and m lie on Plane A. Since l is diagonal and m is horizontal, they are not parallel. However, without additional information on their angles, we cannot say they are perpendicular. Therefore, l and m are neither parallel nor perpendicular.

2. l and n:
   Line l lies on the horizontal Plane A, while Line n is vertical on Plane B. Since l lies on the horizontal plane and n is vertical, these two lines are neither parallel nor perpendicular. Moreover, they lie on different planes, meaning they do not intersect. Hence, l and n are skew lines.

3. m and n:
   Line m is horizontal on Plane A, and Line n is vertical on Plane B. Since n is vertical and m is horizontal, they meet at a right angle, so m and n are perpendicular.

Summary:

• l and m: Neither parallel nor perpendicular.
• l and n: Skew.
• m and n: Perpendicular.

Would you like further details or have any other questions?

Here are 5 related questions to explore further:

1. What conditions are necessary for two lines to be considered skew?
2. Can two lines on the same plane ever be skew?
3. How do we determine if two diagonal lines on the same plane are perpendicular?
4. What is the relationship between two lines that intersect at an angle other than 90 degrees?
5. How does the orientation of planes affect the relationships between the lines?

Tip: To determine if two lines are skew, check if they lie on different planes and do not intersect.