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Vectors

A vector is an element of a vector space, which is a collection of vectors.

In the diagram below, (x,y) and (x,y,z) are vectors.

Vector Magnitude

The magnitude of a vector is equal to its length. This is calculated as the square root of the sum of the squares of its individual coordinates.

Vector Dot Product

A vector dot product:

  • is an algebraic operation that takes two equal-length sequences of numbers

  • returns a single number

  • derives its name from the dot symbol used to designate the operation

  • is the sum of the products of the corresponding entries of the two sequences of numbers

An example is:

Euclidean Vector

A Euclidean Vector is a geometric object that has a magnitude and direction.

References