Is vacuum a Dielectric. If so how? please explain physically and mathematically
Vacuum cannot be considered as a dieletric.
A dielectric is defined as an insulating material which can be polarized by applying electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, but only slightly shift from their average equilibrium positions causing dielectric polarization.
Nothing like that will happen in the case of vacuum.
But in theory, if necessary, vacuum can be considered as a dielectric medium of dielectric constant unity.