freeCodeCamp/guide/english/mathematics/vectors/introduction-to-vectors/index.md

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Introduction to Vectors

Introduction to Vectors.

A vector is a physical quantity that can be measured (has magnitude in units) and also operates in a particular direction, unlike a scalar which can only be measured. Examples of vectors include velocity, acceleration, force and momentum.

A vector can be represented by a line drawn, such that:

  • the length of the line represents the magnitude of the vetor in a given unit;
  • the direction of the line represents the direction in which the vector operates (or acts).

vector-representation

In the figure above, the displacement of A to B is written as AB (ā or a). point A is the origin or initial point and the point B is the head or terminal point. This displacement is equivalent to moving a distance x horizontally followed by y vertically.

The Modulus of a vector

The modulus of a vector is a positive scalar number that gives magnitude of the vector. It is written like this:

 |AB| or |a| or simply AB or a. 

Where;

|AB| =   √(x2 + y2)

More Information:

  1. Euclidean vector.
  2. Vector and Vector Arithmetic.