- If you're working on a single sheet of paper (2-D), then you can
draw four lines that intersect in 1, 2, 3, 4, 5, or 6 points.
- If in 3-D space, then you can also draw four lines that don't intersect at all.
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Yes it can
The greatest number of intersection points with just four lines is 6.
The greatest number is six.
No. In plane geometry, two lines can intersect at at most one point. This means that for n points, the maximum number of intersections is limited by the number of pairs of lines. For lines a,b,c,d, there are six pairs: (a,b), (a,c), (a,d), (b,c), (b,d), (c,d). So four lines can have at most six intersections.
Being 'perpendicular' would require the lines to be at 'right angles' to each other... So, if working in a 2-dimensional setting, the joining of 3 perpendicular lines would not be possible. If working in a 3-dimensional setting, the answer would be 12. Four from the intersection of the 1st and 2nd lines, four from where the 3rd line intersects initially, and four from where the 3rd line leaves the intersection.