Why is the equivalent force-couple system at corner D needed?

[jaredmt]

Homework Statement

A 63lb force F and 560lb in couple M are applied to corner A of the block shown. Replace the given force-couple system with an equivalent force-couple system at corner D

Homework Equations

The Attempt at a Solution

I actually solved the problem but I had to guess and check. I am not sure why it works the way it worked so I was hoping somebody could explain this to me.

First i found the components of M. then I found the components of the Moment created by F by doing A X F. I called this M1
Then I put the same force at point D and did D X F giving me M2

in order to find the answer I had to do M - M1 + M2. Can someone explain why I had to do M - M1 + M2?

 

[nasu]

Can you show the diagram?

The total torque (and total force) should be the same in both cases.

 

[jaredmt]

I don't have a way of getting a good picture of it. but i can give u this info if it helps:
A (0,7.2,4.8)
D (14.4,0,0)
F = <54,27.1,-18>
M (@ point A) = <448,-336,0>
M1 = AXF = <-259.7,259.2,-388.8>
M2 = DXF = <0,259,390.24>