What are the tensions in BC and BD?

[Uninspired]

mass of e is 100 kg
mass of bar is 20 kg and acts at midpoint
sume of moments about point a due to weight of bar and forces on b by bc, bd, and be, are 0, determine tensions in bc and bd

so i continued like this.
The moment about point A from all those forces is 0.
0 = (Raf x Wab) + (Rab x Wbe) -(Rab x Tbc) - (Rab x Tbd)

I can figure out the first two terms of this eq, but i have to find magnitude of the vectors of Tbc and Tbd. But i only have this equation and these two equations:

Tbc= |Tbc|*Ebc where Ebc is a unit vector in BC direction
Tbd= |Tbd|*Ebd where Ebd is a unit vector in the BD direction

Did i set this up incorrectly or how do i proceed?

a picture has been included.

Thanks for your help

Pt A is at the origin
Pt D is (0,5,5)
Pt C is (0,4,-3)
Pt B is (4,3,1)
Pt E is where the 100 kg weight is
AB is the bar where 20 kg acts down the midpoint
any help is APPRECIATED!

 

[Uninspired]

bump, anyone?

 

[Fermat]

You know the position vectors of all the points.
Use vector algebra to work out the vectors AB, DB, CD.
Thes structure is in static equilibrium, therefore
$$\sum F_i = 0$$ $$\sum F_j = 0$$ $$\sum F_k = 0$$

$$\mbox{If}\ \bf{AB} = (x_1,y_1,z_1)\ \mbox{then}\ F_{AB} = \lambda(x_1,y_1,z_1)$$

You should be able to use the above two lines to solve the problem.