Dot product
The dot product of two vectors a and b (sometimes
called the inner product, or, since its result is a scalar, the scalar product) is denoted by a ∙ b and is defined as:
where θ is the measure of the angle between a and b (see trigonometric function for an explanation of cosine).
Geometrically, this means that a and b are drawn with a common start point and then the length of a is multiplied with the length of that component of b that points in the same direction as a.
The dot product can also be defined as the sum of the products of the components of each vector as