Under normal driving conditions, if the front brakes are not operating and the back brakes lock, which way will the vehicle rotate?

When the front brakes are not functioning while the back brakes lock, the vehicle will rotate 180 degrees and will skid backwards. This is due to the dynamics of braking and the distribution of weight in a vehicle.

In a typical braking scenario, the front brakes provide a significant amount of stopping power, as the weight of the car shifts forward when braking. If the back brakes alone lock up, they will cause the rear of the vehicle to pivot around its center of gravity. Since there is no braking force at the front to assist in maintaining traction, the rear wheels losing grip results in a rapid rotation of the vehicle, effectively causing it to spin around.

This phenomenon occurs especially if the back tires are unable to maintain traction while the front tires are free to rotate. The locked rear wheels will skid, leading to a significant rotation which can result in the vehicle facing the opposite direction, effectively turning 180 degrees. The vehicle then continues in reverse as it skids, thus confirming why this answer is the most accurate representation of the situation described.