The word components, in the following context, means parts. So, to talk about the components of a vector, we mean the parts of a vector.
For a great amount of situations the important parts of a vector are it's x-part and its y-part, or its x-component and its y-component. Here we will see how to find the x-component and the y-component of a vector.
The vector we will use in the following discussion is a force vector. The methods shown here, though, are true for any vector, such as a displacement, velocity, or acceleration vector.
Here on the (x, y) set of axes is the force vector that we will be dealing with:
If you drop a line from the tip of the original vector straight down to the x-axis and draw a vector along the x-axis from the origin to where this line hits the x-axis, then this newly drawn vector is the x-component of the original vector. In the diagram the line that was dropped down is shown as a thin black line and the x-component is shown as a red vector:
In the following diagram the thin black horizontal line marks how high up the original vector rises. A vertical vector, (parallel to the y-axis), which rises to this height is called the y-component of the original vector. The y-component is shown below in green:
This right triangle will allow us to to do right triangle trigonometry using SOH-CAH-TOA definitions.