Find a plane in R4 which goes through the point A.

[serict]

Consider the point (1,1,1,1)
1) Find a plane in R4 which goes through the point A.
2) Find 2 planes in R4 whose only intersection point is the point A.
3) Find three planes in R4 such that each planes intersect only in the point A.

 

[tkhunny]

In 2D

2 Lines can Intersect in a single point or infinitely many points or no points. It is important to note that 2 points is not a possible outcome in Euclidean Geometry.

In 3D

2 Lines can Intersect in a Single Point (Since2 Lines determine a plane, this is not different from 2D)
2 Planes can Intersect in a LINE or a PLANE or not at all. "Single Point" is not in this list.

Now, how might we extrapolate this sequence to answer some fundamental questions about 4D.