On the inner product of vector How did the vector inner product formula come from? What's the reason for the inventor to stipulate that, and the vector multiplied by the vector is a constant

On the inner product of vector How did the vector inner product formula come from? What's the reason for the inventor to stipulate that, and the vector multiplied by the vector is a constant

This is from the practice of physics. In physical calculation, it is often used to project a vector to the direction of another vector, and then multiply it by the module of another vector. Moreover, such an algorithm represents a fixed physical meaning. Because of this kind of problem, some people define the inner product in this way, which is for the convenience of writing and intuition