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We study the two-component Ginzburg-Landau (GL) theory, in the presence of a self-consistent vortex line, to obtain the penetration depth (λ) and the effective healing length (ξ), in the asymptotic limit r → ∞. All these parameters versus T/Tc are analyzed for the materials MgB2, V3Si and LiFeAs in the interval 0.88 ≤ T/Tc ≤ 1.0, where the GL theory is assumed to be valid. We find that κ ≡ λ/ξ, which is another parameter not related to the GL parameter, is T-independent for V3Si and LiFeAs, while is T-dependent for the compound MgB2. This result suggests that even though all these three materials display two-gap superconductivity overall, near Tc superconductivity in V3Si and LiFeAs and seems to be different from the one in MgB2. The use of this parameter, κ, as a new way to " study" the superconducting materials, under the presence of a single vortex, is valid for 0.88Tc≲ T ≤ Tc, namely, in the GL formalism. [ABSTRACT FROM AUTHOR]