Why does the scalar product of a vector not satisfy the associative law

Why does the scalar product of a vector not satisfy the associative law

From the formula of the law of association, (a · b) is a number, so the result of (a · b) · C is a vector with the same direction as C, while the direction of the vector calculated by a · (B · C) is the same as a, and the direction is different, so it does not satisfy the law of association