How force is a vector quantity?

Hint: Firstly, you could define both vector and force. The definition should be very clear that we get strong conceptual clarity of the two topics. From the definition of the two terms, you could interrelate the two and hence you could easily understand how we could determine that force is a vector.

Complete answer:
In the question, we are asked why the force is called a vector quantity. In order to answer this question, we have to have a good clarity on the concepts of both vectors as well as the force.

You may recall that a quantity is described as a vector quantity when it is known to have both magnitude as well as direction.

Now let us recall what a force is. Force is defined as the product of mass and acceleration by using the second law of motion. Though mass is a scalar quantity that has only magnitude, acceleration does have both magnitude and direction. So we could say that force is also a vector quantity that has both magnitude as well as direction.

Consider the case of push and pull. The direction of the force applied determines whether it is push or pull. The description of the force acting on a body is incomplete when either magnitude or the direction is not described.

You may recall that the free body diagrams are made assigning the direction of the forces acting on it and then by balancing them we solve the problems.

Note:
Vectors are represented geometrically by arrows normally. The direction in which the arrow is pointing gives the direction of the vector and length gives its magnitude. Two vectors are said to be equal when they are equal both in magnitude as well as direction. Also, the position of the vector doesn’t affect the magnitude and direction of vectors.