Intersection of a 4D line and a 3D polyhedron in 4D

[LCDF]

Is the intersection of a 4D line segment and a 3D polyhedron in 4D a point in 4D, if they at all intersect? Intuitively, it looks like so. But I am not sure about it and how to prove it.

 

[mfb]

If they are not in the same 3D space then the intersection will be a point. You can even use the full 3 D volume and a full line and it will still be a single point.

You can look at the line segment in a coordinate system where the 3D object is aligned with three axes, for example.

 

[LCDF]

Thanks. Is there a mathematical proof for your observation? A hint would also work.

 

[mfb]

My second paragraph is a description how to get to a proof.

It's basically the same as with a plane and a line in 3D, just with one more coordinate.