There are two kinds of vector products, one is quantity product (point multiplication), the other is cross product (cross multiplication) and the other is point multiplication.

Why is the product of two vectors equal to their modulus multiplied by the cotangent of their included angle?

The definition is that one vector A times the projection of another vector B on this vector, which is easy to find.

B*Cos angular multiplication equals modular multiplication, because it is a * * * line.