Dot Product

The dot product of two vectors is obtained by adding the products of the respective components of the vectors.

The dot product of two vectors:

is represented and calculated as:

Commutative law

Distributive law

also

The dot product of a vector with itself is the square of the magnitude:

Note:

if A=0 and only if A=0

Cauchy-Schwarz Inequality

The dot product of two vectors cannot be greater in magnitude than the product of the magnitudes of the vectors.

See also: Vector.