Final answer:
A controller would vector an aircraft in uncontrolled airspace (Class G) to ensure safety and maintain separation between aircraft.
Step-by-step explanation:
In uncontrolled airspace (Class G), a controller would vector an aircraft when necessary to ensure separation and maintain the safety of the airspace. Vectors are provided to assist the pilot in avoiding other aircraft or obstacles in the vicinity. When considering why a controller might vector an aircraft in uncontrolled airspace (Class G), it's important to understand that although Class G is uncontrolled, air traffic control (ATC) may provide services to aircraft for safety reasons.
A controller could vector an aircraft in Class G airspace due to several reasons such as traffic advisories, search and rescue operations, or providing a service to VFR aircraft if workload permits. However, it's crucial to note that pilots flying in Class G airspace are primarily responsible for their own separation and collision avoidance. For example, if there is a potential conflict between two aircraft, the controller may instruct one of the pilots to change their heading or altitude to create sufficient separation. This would avoid a potential collision.