3D Vector Dot Product Calculator

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

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Created: 2019-06-06 05:41:21, Last updated: 2023-02-11 10:33:55
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The dot product or scalar product of two vectors a and b is defined as
\mathbf {a} \cdot \mathbf {b} =\|\mathbf {a} \|\ \|\mathbf {b} \|\cos(\theta ),
\|\mathbf {a} \|\ and \|\mathbf {b} \|\ are the magnitudes of the vectors a and b respectively, and \theta 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.

PLANETCALC, Dot product

Dot product

First vector

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
\mathbf {\color {red}a} \cdot \mathbf {\color {blue}b} =\sum _{i=1}^{n}{\color {red}a}_{i}{\color {blue}b}_{i}={\color {red}a}_{1}{\color {blue}b}_{1}+{\color {red}a}_{2}{\color {blue}b}_{2}+\cdots +{\color {red}a}_{n}{\color {blue}b}_{n},
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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PLANETCALC, 3D Vector Dot Product Calculator