Can Two Planes Meet at a Point Instead of a Line?

[tut_einstein]

Is it possible for two planes to meet in a point instead of in a line?

 

[HallsofIvy]

No. The only possiblities are:
1) Do not intersect. (the planes are parallel)
2) Intersect in a line.
3) Intersect in all points. (They are actually the same plane)

 

[Ben Niehoff]

I have to disagree with HallsofIvy. The answer depends on the dimension of the ambient space in which the planes live.

In 3 dimensions, Halls is correct.

In 4 dimensions and higher, two planes (i.e., 2-dimensional objects) can certainly intersect in a point.

 

[chiro]

I have to disagree with HallsofIvy. The answer depends on the dimension of the ambient space in which the planes live.

In 3 dimensions, Halls is correct.

In 4 dimensions and higher, two planes (i.e., 2-dimensional objects) can certainly intersect in a point.

Are these linear objects you are talking about or some other kind?

 

[blue_raver22]

Yes, it is possible for two planes to intersect at a single point. This occurs when the two planes are not parallel and their normal vectors are not perpendicular to each other. In this case, the two planes will meet at a single point, forming what is known as a "point of intersection." This can be visualized as the point where two sheets of paper, placed at an angle to each other, touch each other at a single point. The concept of two planes intersecting at a point is commonly used in mathematics and engineering, and has practical applications in fields such as computer graphics and 3D modeling.