Force is a vector. Let me illustrate it's use in the following section.
Here is how that Newton's second law appeared in nineteenth century notation,
But, with using vector notation, the equation simply becomes
Acceleration might also be represented similarly.
The three equations are combined to one : a great economy for the three we would need otherwise.
Now, let us consider work done by a force
The work done, is given as
In terms of scalar product, it becomes,
Similarly, if a force
In vector notation and incorporating a direction for the torque, the expression looks like
There are several other vectors which are related to physical problems. EM fields, gravitational fields, force, displacement, acceleration, momentum, torque, all are vectors, just to name a few.