Question

prove that the weight is a vector quantity.

Answer 1

Because weight is the force of gravity acting on an object.

Forces are vectors. A downward force (like weight) is affects a body differently than an upward force (like the floor's normal force). And both of these forces affect a body differently than horizontal forces, like human pushes and pulls, or friction.

Mass by contrast is a scalar. Mass is the amount of material in an object (although a more formal definition exists). Mass exists regardless of gravity's existence. Mass has no directionality.

Do not confuse mass and weight, even though in everyday speech these terms are misused interchangeably

Answer 2

Because weight is the force of gravity acting on an object.

Forces are vectors. A downward force (like weight) is affects a body differently than an upward force (like the floor's normal force). And both of these forces affect a body differently than horizontal forces, like human pushes and pulls, or friction.