What is the definition of component method in physics?

Answer 1

The component method is the concept that you can resolve vectors into two independent (therefore perpendicular) vectors (say, in the x and y directions). And, you can "put a vector back together" simply, using the distance formula and the slope of the line.

So, the component form and the direction/magnitude forms are just two different ways of specifying a vector.

Answer 2

It usually refers to a part of a greater force or other directional quantity. For example for a force in three dimensions, you would have the x component of the force, the y and the z component. Or you might have components more focused on the problem rather than some imposed system of coordinates. For example, when you have an object on a string and you are swinging it around your head you have the component of the force that is changing its direction, the centripetal force, and the component that keeps it moving.