noolvektorid

Noolvektorid, commonly known as directed line segments, are fundamental geometric objects. They possess both magnitude, represented by their length, and direction, indicating where they point. Unlike simple lines, a noolvektor has a specific starting point, called the initial point or tail, and an ending point, called the terminal point or head. This distinction is crucial as reversing the order of the points creates a different noolvektor with the opposite direction. The magnitude of a noolvektor is the Euclidean distance between its initial and terminal points. Geometrically, noolvektorid are often depicted as arrows. In physics and engineering, they are used to represent quantities such as velocity, force, and displacement. Mathematically, noolvektorid can be represented using coordinates. For a noolvektor with initial point $(x_1, y_1)$ and terminal point $(x_2, y_2)$ in a two-dimensional plane, its components are given by $(x_2 - x_1, y_2 - y_1)$. The magnitude can then be calculated as $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Operations such as addition and scalar multiplication are defined for noolvektorid, allowing for manipulation and analysis in various mathematical and scientific contexts.