How Do You Solve This 3D Forces and Moments Problem?

[Wesc]

Forces F1 =j + 3k, F2 = j + k and F3 = 2i + j act at the point (0; 1;2), (1;0;3) and (1;1;0) respectively.
(a) Find the total force and the total moment about the origin.
(b) Find an equivalent system of forces consisting of a single force acting at the (1;0;0) together with a couple.Ok so for (a), I think I have the correct answer. For the total force I simply added up the sum of forces and got a figure of -2i + j + 4k.
Then for the total moments I got the sum of each of the 3 individual moments. I calculated these by computing the determinant of a 3x3 matrix, with the top row being i j k , middle row being 'r' and the bottom row being the force. I got the total moment to be -4i + j + 2k.However, I'm stuck on (b). I don't really know where to start. If someone could write out how to do it I'd appreciate it so much because my Applied Mathematics exam is tomorrow !

 

[rock.freak667]

You'd do it in the same way as part a)

Except you'd need to get the new 'r' vectors from the points to <1,0,0> instead of the origin.

Use r = r_A-r_B