Q20 Matemática  (IMO Longlists 1970)

Seja $M$ um ponto interior do tetraedro $ABCD$. Prove que $$\begin{array}{c}\stackrel{⟶}{\mathrm{MA}}\text{vol}(MBCD)+\stackrel{⟶}{\mathrm{MB}}\text{vol}(MACD)+stackrel⟶MC\text{vol}(MABD)+\stackrel{⟶}{\mathrm{MD}}\text{vol}(MABC)=0\end{array}$$ ($\text{vol}(PQRS)$ denota o volume do tetraedro $PQRS$).