Coordinate systems

A coordinate system is a system that uses one or more numbers, called coordinates, to uniquely determine the position of a point or other geometric elements on 1D, 2D, and 3D dimensions. Each of these numbers indicates the distance between the point and some fixed reference point, called the origin. The first number, known as the \(x\) value, indicates how far left …

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Vector

Vectors are indicated in the scientific literature with a letter, generally lowercase, with an arrow above it: \(\vec{v}\). Vectors are essential to physics and engineering. Many fundamental physical quantities are vectors, including displacement, velocity, force, and electric and magnetic vector fields. In this context, the following fundamental entities are assigned: free vectors: characterized by magnitude, direction, …

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Volume

In geometry, the volume is defined as the measure of space occupied by a three-dimensional body. The volume of a three-dimensional body is a numerical characteristic of the body; in the simplest case, when the body can be decomposed into a finite set of unit cubes (i.e., cubes with edges of unit length), it is equal to …

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Position

In order to describe the motion of an object, you must first be able to describe its position (where it is at any particular time). More precisely, you need to specify its position relative to a convenient reference frame. So the position of a point \(P\) can be described by a pair or a set of coordinates, …

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