Study guides

☆☆

Q: Three lines that intersect in a point but do not all lie in the same plane?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.

If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)

It's possible, but for any three lines in the same plane, there could be ether one point of intersection (unlikely) or three (more probably).

No because only co-linear lines lie on the same plane

In Euclidean plane geometry two infinitely long straight lines intersect at only one point

Related questions

All non-parallel lines in a plane will intersect at some point in the plane.

no

Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.

If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)

No they can be Collinear - Points that lie on the same line.

No, only three lines can intersect at a single point.

No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.

It's possible, but for any three lines in the same plane, there could be ether one point of intersection (unlikely) or three (more probably).

Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.

No. Any pair of the three will describe a plane, so the three possible pairs describe three planes.

false.

concurrent

People also asked