Final answer:
Potential energy is scalar while weight is vector due to the nature of their definitions and equations.
Step-by-step explanation:
Potential energy is scalar while weight is vector according to the equation mgh = wh. Potential energy, specifically gravitational potential energy, is the energy associated with an object's position relative to the ground. It depends on the mass of the object, the acceleration due to gravity, and the height it is lifted through. It is scalar because it possesses magnitude only.
Weight, on the other hand, is a vector quantity that represents the gravitational force acting on an object. It is defined as the product of mass and acceleration due to gravity. Weight has both magnitude and direction as it is a force vector.