3.3.2 Component Vectors

FIGURE 3.10 shows a vector $\vec{A}$ and an xy-coordinate system that we’ve chosen. Once the directions of the axes are known, we can define two new vectors parallel to the axes that we call the component vectors of $\vec{A}$ . You can see, using the parallelogram rule, that $\vec{A}$ is the vector sum of the two component vectors:

\vec{A} = \vec{A}_{x} + \vec{A}_{y}

(3.5)

In essence, we have broken vector $\vec{A}$ into two perpendicular vectors that are parallel to the coordinate axes. This process is called the decomposition of vector $\vec{A}$ into its component vectors.

The figure illustrates the components of a displacement vector labeled vector "A" using the x y coordinate plane.

FIGURE 3.10 Full Alternative Text

NOTE It is not necessary for the tail of $\vec{A}$ to be at the origin. All we need to know is the orientation of the coordinate system so that we can draw $\vec{A}_{x}$ and $\vec{A}_{y}$ parallel to the axes.