Final answer:
In eukaryotic flagella, microtubules slide past one another due to the activity of dynein proteins, allowing the flagellum to bend and propel the cell.
Step-by-step explanation:
In eukaryotic flagella, the fibers that slide past one another due to the activity of dynein proteins are microtubules. These structures are central to cell motility and are part of the cytoskeleton. The eukaryotic flagella contain a 9+2 arrangement of microtubules, with nine outer doublet microtubules and a central pair. The dynein arms attached to the A tubules of the outer doublets move along the B tubules of the adjacent doublet, causing microtubule sliding which enables the flagellum to bend and generate motion.