Vector (geometric) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-04

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Euclidean_vector


00:02:08 1 History
00:05:11 2 Overview
00:07:20 2.1 Examples in one dimension
00:08:08 2.2 In physics and engineering
00:09:24 2.3 In Cartesian space
00:09:43 2.4 Euclidean and affine vectors
00:10:08 2.5 Generalizations
00:11:08 3 Representations
00:11:24 3.1 Decomposition or resolution
00:13:22 4 Basic properties
00:15:24 4.1 Equality
00:18:14 4.2 Opposite, parallel, and antiparallel vectors
00:26:10 4.3 Addition and subtraction
00:28:52 4.4 Scalar multiplication
00:30:34 4.5 Length
00:32:47 4.6 Dot product
00:35:15 4.7 Cross product
00:37:09 4.8 Scalar triple product
00:38:46 4.9 Conversion between multiple Cartesian bases
00:38:49 4.10 Other dimensions
00:40:33 5 Physics
00:40:52 5.1 Length and units
00:41:12 5.2 Vector-valued functions
00:44:38 5.3 Position, velocity and acceleration
00:44:41 5.4 Force, energy, work
00:46:26 6 Vectors as directional derivatives
00:49:40 7 Vectors, pseudovectors, and transformations
00:52:54 8 See also
01:09:01 9 Notes
01:14:49 10 References
01:15:03 10.1 Mathematical treatments
01:16:04 10.2 Physical treatments
01:16:45 11 External links
01:17:51 (x1, x2, x3), y
01:20:11 Force, energy, work
01:21:04 Vectors as directional derivatives
01:24:12 Vectors, pseudovectors, and transformations
01:25:22 Mx, then a contravariant vector v must be similarly transformed via v′
01:28:16 See also



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SUMMARY
=======
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by 
  
    
      
        
          
            
              A
              B
            
            →
          
        
        .
      
    
    {\displaystyle {\overrightarrow {AB}}.}
  
A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun.  The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.
Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.