Chapter 15.P, Problem 4P

If a, b, and c are constant vectors, r is the position vector $xi\text{+}yj\text{+}zk$, and E is given by the inequalities $0\le a\cdot r\le \alpha ,0\le b\cdot r\le \beta ,0\le c\cdot r\le \gamma$, show that

${\displaystyle \underset{E}{\iiint }\left(a\cdot r\right)\left(b\cdot r\right)\left(c\cdot r\right)dV=\frac{{\left(\alpha \beta \gamma \right)}^2}{8\left|a\cdot \left(b\times c\right)\right|}}$