Question

Vector definition of mathematics wolfram

Answer 1

A vector is formally defined as an element of a vector space. In the commonly encountered vector space  (i.e., Euclidean n-space), a vector is given by  coordinates and can be specified as . Vectors are sometimes referred to by the number of coordinates they have, so a 2-dimensional vector  is often called a two-vector, an -dimensional vector is often called an n-vector, and so on.

Vectors can be added together (vector addition), subtracted (vector subtraction) and multiplied by scalars (scalar multiplication). Vector multiplication is not uniquely defined, but a number of different types of products, such as the dot product, cross product, and tensor direct product can be defined for pairs of vectors.

A vector from a point  to a point  is denoted , and a vector may be denoted , or more commonly,. The point  is often called the "tail" of the vector, and  is called the vector's "head." A vector with unit length is called a unit vector and is denoted using a hat, 

When written out componentwise, the notation generally refers to On the other hand, when written with a subscript, the notation (or  generally refers to

An arbitrary vector may be converted to a unit vector by dividing by its norm (i.e., length; i.e., magnitude)