  Schmidt generalized in 1967 the theory of classical Diophantine approximation
to subspaces of $\R^n$. We consider Diophantine exponents for linear subspaces
of $\R^n$ which generalize the irrationality measure for real numbers. Using
geometry of numbers, we construct subspaces of $\R^n$ for which we are able to
compute the associated exponents for the last angle.
