DISPLACEMENT AS A VECTOR
 

When displacement is defined in a straight line, it is a vector quantity because it has both magnitude (expressed in meters, kilometers, or other distance units) and direction (which can be defined in various ways). Displacement magnitude is denoted by a lowercase italicized letter; let’s call it q. A displacement vector is denoted by a lowercase boldface letter. In this discussion, let’s use q.
The displacement vector qrm of Minneapolis relative to Rochester would be approximately 100 km in a northwesterly direction “as the crow flies.” As an azimuth bearing, it would be around 320 degrees, measured clockwise from true north. However, if we speak about driving along Route 52, we can no longer define the displacement as a vector because the direction changes as the road bends, goes over hills, and dips into valleys. In this case, we must denote displacement as a scalar, usually in lowercase italics. In this discussion let’s use q. We write q_rm ≈ 120 km.