Force supported by cable and struts with load in multiple planes

[CB4]

Homework Statement

A 1125 N force F is supported by cable AD and by struts AB and AC as shown. If the struts can transmit only axial tensile or compressive forces, determine the forces in the struts and the tension in the cable.

a = 6 m

b = 1 m

c = 4 m

d = 6 m

f = 2 m

[PLAIN]http://img714.imageshack.us/img714/773/cbb026135set3dconcurren.png

The Attempt at a Solution

Well I set everything up by first finding vectors AD, AB, and AC, which come out to be, respectively, <0,6,4>, <-1,6,-2>, <4,6,-2>. I then proceeded to solve for the Force vectors by components and got:

(vec)Fad = 0i(Fad) + .83205j(Fad) + .5547k(Fad)
(vec)Fab = -.156174i(Fab) + .93704j(Fab) - .31235k(Fab)
(vec)Fac = .53452i(Fac) + .80178j(Fac) + .26726k(Fac)

Then I set them up for a matrix

(Sum)Fx = 0i(Fad) - .156174i(Fab) + .53452i(Fac)
(Sum)Fy = .83205j(Fad) + .93704j(Fab) + .80178j(Fac)
(Sum)Fz = .5547k(Fad) - .31235k(Fab) + .26726k(Fac)

The problem that I am having is that the given force of 1125 N lies in both the z and y planes. How exactly do you implement that force into your equations to solve for the variables?

 

[nvn]

F = 0*i + 0*j - 1125*k.

CB4: When you determined vectors AB and AC in post 1, I am not yet understanding why you listed the z component as negative.

By the way, when you talk about a plane, you must use two letters to describe the plane (xy, yz, or xz). Therefore, I do not know which planes you are referring to in your question, because you only used one letter. F lies in only one plane, the yz plane.