The answer is the second one (b): processing location and motion; problems would make it difficult to balance.
Explanation for each option:
a. Encoding and processing faces; problems would make it difficult to recognize friends: This is incorrect. The vestibular system is not involved in facial recognition. Facial recognition is primarily associated with the fusiform gyrus in the brain.
b. Processing location and motion; problems would make it difficult to balance: This is correct. The vestibular system is responsible for providing the brain with information about motion, head position, and spatial orientation. It helps maintain balance and posture.
c. Transforming chemical smells into electrical signals; problems would make it difficult to smell: This is incorrect. The olfactory system is responsible for the sense of smell, not the vestibular system.
d. Sending pain and temperature signals from the skin to the brain; problems would make it difficult to feel pain: This is incorrect. The somatosensory system is responsible for processing sensory information such as pain and temperature, not the vestibular system.
In summary, the vestibular system is primarily responsible for processing location and motion, which is crucial for maintaining balance.