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