Two subspaces UUU and WWW of VVV satisfy U∩W={0}U \cap W = \{0\}U∩W={0}. What can we conclude?
The sum U+WU+WU+W is a direct sum.
UUU and WWW must be orthogonal.
The dimension of U+WU+WU+W is dim(U)+dim(W)+1\dim(U) + \dim(W) + 1dim(U)+dim(W)+1.
UUU must be a subset of WWW.