Is Net Internal Torque Really Zero in All Cases?

[tukms]

I have a confusion of a conclusion in the textbook ( I posted it in the attach file )

Net internal torque equals zero ( similarly to conclusion in the Newton’s third law ) but I myself reckon that torque is defined as
${\rm{r \times F}}$
And maybe there occurs the case below :
${\rm{F}}_{{\rm{21}}} {\rm{ = - F}}_{{\rm{12}}} $
But
${\rm{r}}_{21} {\rm{F}}_{{\rm{21}}} \ne {\rm{r}}_{12} {\rm{ - F}}_{{\rm{12}}} $

Could someone help me analyze this situation , I think that the conclusion in textbook is true but it is still fuzzy for me
Thank you in advance

 

[aim1732]

I wish your code made more sense.
Torque of internal forces is not accounted because the net resultant of the radius vectors is along the line of action of the force.
Considering two particles 1 and 2 on the rigid body. Let their position vectors be r₁ an r₂.Let no external torque act for simplification.
Then Γ_net = r₁ × F₁₂ + r₂ × F₂₁
You know F₁₂=-F₂₁ by Newton's Third Law.
Hence Γ_net =(r₁-r₂) × F₁₂
r₁-r₂ will be along the line joining the two particles and this is also the line of action of the force b/w the two particles[F₁₂]. Since angle is 0 there is no torque.
I hope this is useful.