Final answer:
The motor protein ciliary dynein drives the bending of microtubules in the eukaryotic flagellum by causing the microtubules to slide past one another, resulting in the bending motion required for cellular locomotion.
Step-by-step explanation:
In the eukaryotic flagellum, the bending of microtubules is driven by the motor protein ciliary dynein. These dynein arms are attached to the A tubules of the outer doublets in the axoneme and they 'walk' along the B tubules of the adjacent doublet. As a result of this walking motion, the microtubules slide past one another, and due to restraints by nexin and radial spoke attachments, the axoneme bends. This mechanism is critical for the movement of both cilia and flagella in eukaryotic cells.