Dot product
This online calculator calculates the dot product of two vectors
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 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
First vector
Second vector
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
ai 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.
Similar calculators
PLANETCALC, Dot product
Comments