We have carried out variational calculations of the properties of a quantum vortex line 4He using a shadow wave-function, which generates a distributed vorticity. Based on these calculations we present a microscopic of study the binding of a single 3He to the vortex using both the Lekner-Feynman formalism and a correlated variational wave-function. Both approaches predict that the impurity should be bound. Lekner-Feynman model, however, does not appear to describe correctly some of the correlation effects within the vortex core. To remedy this defect, we propose a variational wave-function, and a preliminary calculation based on it predicts a binding energy in agreement with experiment.