# 3D Vector Dot Product Calculator

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

### This page exists due to the efforts of the following people:

#### Timur

Created: 2019-06-06 05:41:21, Last updated: 2023-02-11 10:33:55 This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8244/. Also, please do not modify any references to the original work (if any) contained in this content.

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.

#### Second vector

Digits after the decimal point: 2
Dot product

### The algebraic definition of the dot product

The dot product may also be defined algebraically as

where
ai 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.

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