Choosing Coordinate Axes

While any choice of direction for the coordinate system will result in the same answer, chosing the axes carefully will make solving the resulting equations easier. Here are two suggestions:

If the quantity you are seeking is the magnitude of a vector, then rotate the coordinate system so that one of the axes is parallel to the vector.
Otherwise, choose the axes so that as many vectors as possible line up with either the x- or y-axis.

For example, in the diagrams below, where the heavy arrows are vectors and the light arrows are coordinate axes, if you are seeking the magnitude of the vector that points downward, then the coordinate system shown on the right is the better choice. If you are seeking the duration of a time interval, then the coordinate system on the left would be the better choice.

Note: these are good general rules of thumb, but they do not always give the most efficient choice. In a few cases, Andes might recommend a choice of axes that does not accord with these rules.