  The positive vector optical tomogram fully describing the quantum state of
spin 1/2 particle without any redundancy is introduced. Reciprocally the vector
symplectic tomogram and vector quasidistributions $\vec W({\mathbf q},{\mathbf
p})$, $\vec Q({\mathbf q},{\mathbf p})$, $\vec P(\vec\alpha)$ are introduced.
The evolution equations for proposed vector optical and symplectic tomograms
and vector quasidistributions for arbitrary Hamiltonian are obtained. The
quantum system of charged spin 1/2 particle in arbitrary electro-magnetic field
is considered in proposed representations and evolution equations which are
analogs of Pauli equation are obtained. The propagator of evolution equation in
the case of homogeneous and stationary magnetic field in Landau gauge is found
and the evolution of initial entangled superposition of lower Landau levels in
the vector optical representation is considered. The system of linear quantum
oscillator with spin in vector optical tomography representation is considered
and the evolution of initial entangled superposition of two lower Fock states
and spin-up, spin-down states is studied in this representation.
