Angular distributions are measured for individually resolved v′, j′ states of HF produced by F + H2 → HF(v′ = 1, j′) + H and F + H2 → HF(v′ = 2, j′) + H reactive collisions in a crossed-beams scattering apparatus. Simultaneous resolution of the HF vibrational and rotational states is achieved spectroscopically for the first time, using laser excitation in conjunction with bolometric detection. The technique is sensitive to population differences between v′ = 1, j′ and v′ = 2, j′ - 1 states optically coupled by specific P2(j′) lines of a vibrotational chemical laser. The measurements are greatly facilitated by the development of a new high-temperature atomic fluorine beam source, which exhibits excellent stability, very high intensity, and narrow velocity distributions. Features common to individual product rotational states are as follows: strong backward scattering into v′ = 2, j′; weaker backward scattering into v′ = 1, j′; and heretofore unobserved scattering into v′ = 1, j′ in the forward hemisphere. These angular distributions agree qualitatively with predictions from fully three-dimensional exact quantum reactive scattering calculations (Castillo et al., J. Chem. Phys. 1996, 104, 6531) that were conducted on an accurate potential energy surface (Stark and Werner, J. Chem. Phys. 1996, 104, 6515). However, quasi-classical calculations conducted on the same potential energy surface do not produce any substantial forward-scattered HF in v′ = 1 (Aoiz et al., Chem. Phys. Lett. 1994, 223, 215), suggesting that its appearance in the forward hemisphere may be a quantum effect. The quantum theoretical cross-sections also suggest that the forward v′ = 1 products arise almost entirely from H2 reactants initially in j = 1.