Chapter 14.7, Problem 47ES

The three-variable analog of the formula derived in part (b) of Exercise 43 is $\frac{\partial \left(x,y,z\right)}{\partial \left(u,\upsilon ,w\right)}\cdot \frac{\partial \left(u,\upsilon ,w\right)}{\partial \left(x,y,z\right)}=1$ Use this result to show that the volume V of the oblique parallelepiped that is bounded by the planes $x+y+2z=\pm 3,x-2y+z=\pm 2,4x+y+z=\pm 6$ is $V=16.$