Do planes in multi-dimensional spaces rarely interact?
Do planes in multi-dimensional spaces rarely interact?
The plane $\{(x,y,1,0,0)\}$ and the plane $\{(0,0,0,z,w)\}$ have empty intersection. This is typical, in the sense that in any reasonable parametrization ("moduli space") for such pairs of planes, the set of pairs with empty intersection is open and dense.