4.1:
Position and Displacement Vectors
Consider a fly in motion. To locate its position in a three-dimensional space, a Cartesian coordinate system is used, and the unit vectors along the axis provide its direction.
The vector arrow which extends from the origin to the object's location is the position vector. It can be represented in terms of the unit vectors.
The position vector is the sum of the vector components on each axis and their magnitudes provide the position along each axis.
If the fly continues its motion, its position vector changes, and the vector difference between the position vectors is called the displacement vector, Δr, which represents the change in position.
For example, if the fly is at point A, and after time t, it reaches point B, then using the position vectors of A and B, the displacement vector of the fly for time t can be obtained.
4.1:
Position and Displacement Vectors
To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
Further, several important kinds of motion take place in two dimensions only—that is, in a plane. These motions can be described with two components of position, velocity, and acceleration. If an object moves relative to a frame of reference, then the object's position changes; this change in position is called displacement. The word displacement implies that an object has moved or has been displaced. Since displacement indicates direction, it is a vector and can be either positive or negative, depending on the choice of direction. Also, an analysis of motion can have many displacements embedded in it, and many applications in physics can have a series of displacements. Thus, the total displacement is the sum of the individual displacements, which should be evaluated carefully using vector addition.
This text is adapted from Openstax, University Physics Volume 1, Section 4:1 Displacement and Velocity Vectors.