Final answer:
The accessory nerve, also known as the spinal accessory nerve, runs over the longus colli muscle. It innervates the sternocleidomastoid and trapezius muscles, which are important for head movement. The accessory nerve receives motor input from the spinal cord and contributes to elevating the scapula and clavicle.
Step-by-step explanation:
The nerve that runs over the longus colli muscle is the accessory nerve, also known as the spinal accessory nerve. This nerve innervates the sternocleidomastoid and trapezius muscles, which are important for changing the position of the head. The accessory nerve receives motor input from the spinal cord and contributes to elevating the scapula and clavicle through the trapezius muscle.