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In the given figure, to identify all the lines perpendicular to \( QR \), we need to find lines that intersect \( QR \) at a right angle (90 degrees). Observing the cube and the orientation of \( QR \), the lines perpendicular to \( QR \) are:

1. \( NR \)
2. \( PR \)
3. \( PM \)
4. \( PL \)

These lines are perpendicular to \( QR \) based on the 3D arrangement of the cube.

Would you like further explanation on how these perpendicular relationships are determined?

Here are five related questions:
1. What are all the lines parallel to \( QR \)?
2. How can you determine the angles between two lines in 3D space?
3. What is the relationship between perpendicular lines and planes in 3D geometry?
4. How would you find the length of \( QR \) given coordinates?
5. What other properties of cubes can be derived from perpendicular lines?

**Tip:** In a 3D figure, lines that intersect at a 90-degree angle within the same plane are perpendicular, especially in structured shapes like cubes.

Identify all the lines perpendicular to QR in the given 3D figure of a cube.

Discover how to identify all lines perpendicular to QR in a 3D cube figure. This geometry problem explores concepts of perpendicularity in 3D space, perfect for students in Grades 8-10.

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