That is, the geometric product is the sum of the symmetric interior product and antisymmetric exterior product. With a negative square it cannot be a scalar or vector quantity, so it is a new sort of object, a bivector.

What is geometry of product?

In mathematics, the geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements called multivectors, which contains both the scalars and the vector space .

What is the difference between geometric and algebraic vectors?

Algebraic - Treats a vector as set of scalar values as a single entity with addition, subtraction and scalar multiplication which operate on the whole vector. Geometric - A vector represents a quantity with both magnitude and direction.