What is dot product? In this video, Professor Walter Lewin presents the dot or scalar product between two vectors. In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space