cdobe,
Forces in the linguistic sense are not defined as vectors. "forces of nature" or "economic forces" are insubstantial concepts. But when we talk about physical forces in the real world, they are indeed defined by vectors.
from merriam webster:
1force noun \ˈfȯrs\
Definition of FORCE
1a (1) : strength or energy exerted or brought to bear : cause of motion or change : active power <the forces of nature> <the motivating force in her life> (2) capitalized —used with a number to indicate the strength of the wind according to the Beaufort scale <a Force 10 hurricane>
b : moral or mental strength
c : capacity to persuade or convince <the force of the argument>
2a : military strength
b (1) : a body (as of troops or ships) assigned to a military purpose (2) plural : the whole military strength (as of a nation)
c : a body of persons or things available for a particular end <a labor force> <the missile force>
d : an individual or group having the power of effective action <join forces to prevent violence> <a force in politics>
e often capitalized : police force —usually used with the
3: violence, compulsion, or constraint exerted upon or against a person or thing
4a : an agency or influence that if applied to a free body results chiefly in an acceleration of the body and sometimes in elastic deformation and other effects
b : any of the natural influences (as electromagnetism, gravity, the strong force, and the weak force) that exist especially between particles and determine the structure of the universe
5: the quality of conveying impressions intensely in writing or speech <stated the objectives with force>
Definitions 1 and 4 are the primary ones we are discussing right now. 1 describes anything that actively moves another thing. That's a pretty broad definition of Force. 4 is the vector quantity we are discussing, by definition. If you understand what 4 means, then that actually very accurately frames definition 1. You have to define what it means to move something else, and that would be a change in momentum.
http://en.wikipedia.org/wiki/ForceFrom wikipedia:
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. Force can also be described by intuitive concepts such as a push or pull. A force has both magnitude and direction, making it a vector quantity. Newton's second law, F=ma, was originally formulated in slightly different, but equivalent terms: the original version states that the net force acting upon an object is equal to the rate at which its momentum changes.[1]
Now do you understand?
For our discussions, we do not need rigorous mathematical vectors, but we do need to understand that every force, displacement, velocity, momentum, all have a direction to them. Energy has no direction, but has an associated momentum when it manifests as kinetic energy.