The definitions of spin orientation and polarization vectors are introduced within the particle density matrix of scattering states in leads. It is shown that spin-density vector can be defined by the product of the spin orientation vector, being a unit direction vector, and the charge density, corresponding to the amplitude of the spin-density vector, experimentally observable by a spatial charge modulation measurement. When an electron transports through a ballistic semiconductor nanostructure, due to quantum interference of two spin eigenmodes, the electron spin generally undergoes nutation on its precession around the effective magnetic field resulting from spin-orbit interactions. The nutation of electron spin is found to be crucial for spin polarization in the quantum transport. When one of two spin-dependent channels in leads is evanescent, electron spin is shown to be fully polarized for distance from the interface larger than the spin precession length.