We probe the gravitational force perpendicular to the Galactic plane at the position of the Sun based on a sample of red giants, with measurements taken from the DR3 Gaia catalogue. Measurements far out of the Galactic plane up to 3.5 kpc allow us to determine directly the total mass density, where dark matter is dominant and the stellar and gas densities are very low. In a complementary way, we have also used a new determination of the local baryonic mass density to help determine the density of dark matter in the Galactic plane at the solar position. For the local mass density of dark matter, we obtained $ dm $0.0008\,M$_ $ = 0.486 pm 0.030 Gev\ $. For the flattening of the gravitational potential of the dark halo, it is $q_ phi,h For its density, $q_ rho,h $=0.781pm 0.055.