In E. coli homologous recombination, a filament of RecA protein formed on DNA searches and pairs a homologous sequence within a second DNA molecule with remarkable speed and fidelity. Here, we directly probe the strength of the two-molecule interactions involved in homology search and recognition using dual-molecule manipulation, combining magnetic and optical tweezers. We find that the filament's secondary DNA-binding site interacts with a single strand of the incoming double-stranded DNA during homology sampling. Recognition requires opening of the helix and is strongly promoted by unwinding torsional stress. Recognition is achieved upon binding of both strands of the incoming dsDNA to each of two ssDNA-binding sites in the filament. The data indicate a physical picture for homology recognition in which the fidelity of the search process is governed by the distance between the DNA-binding sites.