A Vector is a physics term used to describe a quantity with a magnitude (amount) and direction (angle of application). For example, force is a vector quantity. It has an amount (measured in pressure, tension, weight lifted, strain etc..) and a direction (which way the force is being applied).
When someone is squatting, the barbell is applying a downward force on the body (thanks to gravity). The magnitude is determined by the load on the bar and the direction is determined by the placement of the bar.
The person holding the bar is also applying a force. When not moving (in a static position), the force the person is applying upward is equal to that of the force the barbell is applying downward. Because the forces are equal, no movement is occurring.
If the person begins to produce more force than the barbell, then the bar will move upward. If the barbell produces more force than the person, then it will move downward.
side note: The person is also applying a force into the ground (ground reaction force), which in turn propels the person upward and allows for a force to be applied into the bar
Detailed video discussing free body diagrams (extra material)
Body Positions and Vectors (how they influence muscles)
Barbell Bench Press
The barbell bench press is done with the body laying in a supine position (on your back) with your upper half of the body parallel to the earth’s surface (on a flat bench). Because gravity works in straight line (pushing downwards), we know that when we move the barbell we have to move it against gravity (upwards). Depending on how the body is positioned (parallel to the ground) we can determine how the vectors will generally influence the muscle producing the upward force (not talking about bracing muscles).
Generally speaking, this explains why the bench press emphasizes the chest more than an incline press.
Vertical forces are produced by the horizontal adduction on the arms and extension of the triceps (overly simplified for the sake of the example). By keeping the elbows “tucked” to the body, you eliminate some adduction of the arms, which is why narrow grip bench has a greater tricep emphasis.
See example picture below
My arms are essentially acting vector lines representing the force vectors of the movement
Barbell Incline Press
The barbell incline press is done in the same vertical fashion (upward against gravity), but this time we situate our body in a different position (on the incline bench). By changing our body position, we change how the same vertical force vectors of gravity are acting on our body.
Theoretically, if we could manipulate gravity, we could work against different force vectors in the same position. In essence, this is what machines do. This is why you can do a machine row in a position (standing with an erect posture) that you could never do a dumbbell row in. Instead with dumbbells, you have to move your body to fit gravity’s force vectors.
Generally speaking, by moving our body’s position we are now putting greater emphasis on our shoulders and triceps and less on our chest. The vertical force vectors of the person are predominantly being created by more vertical adduction of the shoulder and extension of the arm.
Yes, this is an overly simplified example of how movements work, but it is a necessary step to start to understand what exactly influences our movements. Instead of thinking about exercises in forms of equipment, we should look at exercises in its most basic applicable forms (force vectors). Obviously there is much more that goes in to movement than just force vectors and all of those other areas should be explored, but it would be erroneous to ignore the fundamental principles of physics.