We all know that force and torque are physical quantities which we have defined according to our purpose of work. Now we are all aware that Newton's Second Law from his Laws of Motion states how to measure force i.e. what is the magnitude of force yields the answer $\vec F=m\vec a$. This is a law stated by Newton, and like all laws, it requires no proof and no deduction.
But which law or postulate or corollary states that torque should be equal to $\vec \tau=\vec r \times \vec F$? If not, then why are we sure that the magnitude of torque is actually that only and nothing else? Anyone could have calculated torque by some other formula.
Any help is welcome.
EDIT: According to Resnick-Halliday-Krane, there is something called Newton's Second Law of Rotation which states that $\vec \tau=\vec r \times \vec F$. Is it right?