Is it possible to draw 7 lines which are perpendicular to each other?
No, it is not possible to draw 7 lines that are perpendicular to each other in a 3-dimensional space.

In a 3-dimensional space, three mutually perpendicular lines can be drawn, forming a 3D coordinate system. Any additional line drawn perpendicular to these three lines will lie in one of the three planes defined by these three lines.

Therefore, if we draw four lines that are perpendicular to each other, we can form a 3D coordinate system, and any additional line drawn perpendicular to these four lines will lie in one of the three planes defined by these four lines.

Similarly, if we draw five lines that are perpendicular to each other, we can form a 3D coordinate system and any additional line drawn perpendicular to these five lines will lie in one of the three planes defined by these five lines.

We can continue this pattern and see that any number of lines greater than three that are perpendicular to each other must lie in one of the three planes defined by the previous set of perpendicular lines. Therefore, it is not possible to draw 7 lines that are perpendicular to each other in a 3-dimensional space.
Are there any n-dimensional euclidean spaces where 7 lines that are all mutually perpendicular can exist? If so, what are the restrictions on n.