# 3D Vector Dot Product Calculator

This online calculator calculates the dot product of two 3D vectors

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

where

and are the magnitudes of the vectors **a** and **b** respectively, and is the angle between the two vectors.

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 calculator for calculating the dot product of two three dimensional vectors would require the user to enter the x, y, and z coordinates of each vector, and then it would use the dot product formula above to calculate and display the result.

### The algebraic definition of the dot product

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 the latter is very simple to calculate.

#### Similar calculators

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**PLANETCALC, 3D Vector Dot Product Calculator

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