What is meant by a component of a vector?

Answer 1

A component of a vector can be thought of as an "effectiveness" of that vector in a given direction. It's actually a "piece" or "part" of the vector. A vector is a geometric object with the two characteristics of direction and magnitude. It is when we plot these in a coordinate system that we see the components appear. If we draw a graph with the standard x and y coordinates handed down to us from Descartes, we can more easily see the components. On the graph, draw a vector from the origin (0,0) to the point (5,5). We set the origin as the point of initiation of the vector, and the "little arrow" on the "head" or terminus of the vector is at (5,5). But that vector represents the sum of two other vectors. One is the vector from the origin that runs along the x-axis to (5,0) and the other is the vector that runs from the origin along the y-axis to (0,5). As stated, the sum of these other two vectors makes the original vector we drew. And each of these vectors, the x and y vectors we drew, is a component of the vector we are inspecting. The components of vectors can be expanded into a multitude of dimensions, and will be dependent on the system we use to plot them. Wikipedia has some additional information, and a link is provided.