# Dot product

This online calculator calculates the dot product of two vectors

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The calculator below calculates the dot product of two vectors from vector coordinates using algebraic definition. The dot product definitions, both geometric and algebraic, can be found below the calculator.

### Dot product

The **dot product** or **scalar product** of two vectors a and b is defined by

where

denotes the magnitude of a vector **a**,

is the angle between **a** and **b**

The name "dot product" is derived from the centered dot " · " that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar, rather than a vector, as is the case for the vector product in three-dimensional space.^{1}

The dot product may also be defined algebraically as

where

**a _{i}** is the

*i*-th coordinate,

**n**is the dimension of the vector space

The geometric definition and algebraic definition are equivalent, while latter is very simple to calculate.

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