ILL 1970 Problem 20

Let $M$ be an interior point of the tetrahedron $ABCD$. Prove that $$\begin{array}{c}\ \stackrel{\longrightarrow }{MA} \text{vol}(MBCD) +\stackrel{\longrightarrow }{MB} \text{vol}(MACD) +\stackrel{\longrightarrow }{MC} \text{vol}(MABD) + \stackrel{\longrightarrow }{MD} \text{vol}(MABC) = 0 \end{array}$$

($\text{vol}(PQRS)$ denotes the volume of the tetrahedron $PQRS$).