## Mathematical Analysis## Vector and Other Analyses |

## How can vectors be represented in various dimensional space? |

The length of this vector is 5.0 (see above to determine how to solve for length of the vector); or |V| = 5.0. Thus, the value of the normalized vector is given by:

In this case, 0.6 squared equals 0.36; 0.8 squared equals 0.64. Both added together with the zero equals 1. (If the vector is already normalized, then the value of |V| will be equal to one, and after division the vector will remain as it was before.)

Vectors can be found in two-, three-, or multi-dimensional space. Two-dimensional vectors are seen visually on a graph as a line with an arrow connecting two points. A two dimensional vector is defined by length and direction measured by the angles that the arrow makes with the *x* and *y* coordinate system axes; a vector in such a coordinate system is written as two components, (*x*, *y*).

Vectors in a three-dimensional space are represented with three numbers, one along each coordinate axis. These are the coordinates of the arrow point, usually as *(x, y, z)* if the arrow starts at the origin. A more complex vector is one with multiple components, in which several different numbers in ordered *n*-tuples represent a vector. For example, (4, 1, -2, 0) is an ordered 4-tuple representing a vector in four dimensions.