We compute the Hausdorff dimension of the set of
ψ
\psi
-exactly approximable vectors, in the simultaneous case, in dimension strictly larger than
2
2
and for approximating functions
ψ
\psi
with order at infinity less than or equal to
−
2
-2
. Our method relies on the analogous result in dimension
1
1
, proved by Yann Bugeaud and Carlos Moreira, and a version of Jarník’s theorem on fibres.