We study the decay of Alfven waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfven and slow waves. These interactions have previously been studied separately in long-and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfven waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 x 10(-4) less than or similar to rho(i)k(0 perpendicular to) less than or similar to 1, where the decay is essentially 3D and nonlocal, generating product Alfven and slow waves around the ion gyroscale. Here.i is the ion gyroradius, and k(0 perpendicular to) is the pump Alfven wavenumber. It appears that, except for the smallest wavenumbers at and below rho(i)k(0 perpendicular to) similar to 10(-4) in Channel I, the nonlinear decay of magnetohydrodynamic Alfven waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfven waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfven waves can still be approximately described as normal Alfvenic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.