The types of problems we will be working with involve displacement vectors on the x-y plane. A displacement vector can be specified in two different ways:
All of the problems involve converting from one vector expression to the other. For example, when traveling on the earth's surface you might move in a straight line for a distance of 30 km, in a particular direction:
The diagram on the left shows the vector direction measured with respect to the x-axis (the E-W line); this axis is called the reference axis. The diagram on the right shows the same vector's direction specified with the y axis (N-S line) as the reference. Both diagrams follow method 1 above: distance and heading.
The jargon used for reciting the vector heading takes a little getting used to. The left side diagram shows a heading recited as "26o north of west". This means that the traveler should start by facing west (along the x reference axis), then turn toward north through the specified angle, and go.
Likewise, the right-side diagram is a heading "64o west of north".