3D Vector Dot Product Calculator

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.

Dot product

First vector

x

y

z

Second vector

x

y

z

Calculation precision

Digits after the decimal point: 2

Calculate

Dot product

 

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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.