Final answer:
The British restricted Western settlement beyond the Appalachian Mountains in 1763 to prevent hostilities with Native American tribes, consolidate control over the acquired territories, and limit westward expansion.
Step-by-step explanation:
The reason for British restriction of Western settlement beyond the Appalachian Mountains in 1763 was to prevent further hostilities with Native American tribes in the Ohio River Valley. The British government established an Indian Reserve beyond the Appalachians to consolidate control over the recently acquired territories following the French and Indian War, and to maintain better control over trade and resources in the newly acquired territories. The restriction was also meant to limit westward expansion and the potential for conflict with the French.