Final answer:
The total force exerted by the three dogs cannot be determined with the information provided because forces are vector quantities and we need information on magnitude and direction for all forces involved.
Step-by-step explanation:
In the problem where three dogs are pulling on a wagon, and only one dog's force is known, it is impossible to determine the total force exerted by all three dogs without additional information on the other two dogs' forces and the angles at which they are pulling. This is because forces are vector quantities, which means they have both magnitude and direction, and the total force is found by vector addition of these individual forces.