Positionvektoren

Positionvektoren, often abbreviated as "pos" or denoted by a bold letter like **r**, are fundamental concepts in vector calculus and physics. A positionvektor describes the location of a point in space relative to a chosen origin. It is a vector quantity, meaning it has both magnitude and direction. In a two-dimensional Cartesian coordinate system, a positionvektor from the origin (0,0) to a point (x,y) can be represented as the vector <x,y>. Similarly, in three dimensions, a positionvektor from the origin (0,0,0) to a point (x,y,z) is represented as <x,y,z>.

The origin is a crucial reference point. If the origin is shifted, the components of the positionvektor will change, even though the physical location of the point in space remains the same. Positionvektoren are used to define the trajectory of moving objects, where the positionvektor changes with time. They are also essential in describing the relative positions of multiple objects, by subtracting their respective positionvektoren. For instance, the vector from point A to point B can be found by taking the positionvektor of B and subtracting the positionvektor of A. This concept simplifies many geometric and kinematic problems.