Final answer:
When bowing the head, the sternocleidomastoid is the prime mover that flexes the neck, and the splenius cervicis act as the antagonist opposing this action.
Step-by-step explanation:
When bowing your head to look at your toes, the sternocleidomastoid muscles contract to flex the neck, which is their primary action. Given that the splenius cervicis muscles extend the neck, they would serve as the antagonists to this movement because their action is the opposite of neck flexion. Therefore, the relationship between these muscles while bowing your head is that the sternocleidomastoid is the prime mover, being actively engaged in performing neck flexion, while the splenius cervicis act as the antagonists as they would generally perform the opposite action of neck extension.