What is the tension in the rope attached at -4mxˆ?

[mrcheeses]

Homework Statement

A 100kg mass is supended by 3 ropes. one rope is attached at a point 1mxˆ + 1myˆ, one is attached at 1mxˆ - 1myˆ and one is attached at -4mxˆ. The three ropes all connect at -1mzˆ, at which point the mass is attached. What is the tension T in the rope attached at -4mxˆ?

Homework Equations

Fnet=0
Fg=mg

The Attempt at a Solution

I have no idea how to do this. Do I need to find the angles in between each rope?

 

[voko]

You should represent the tension of each rope vectorially. Which is not hard, as you are given the coordinates of each rope's endpoints, and the rope is a straight line between the endpoints.

 

[shutdo]

If you bother with the angle and different planes, you could, but it is more convenient to solve this with vectors.
First, you need to set up vector equations for the 4 forces involved.
Since you can work out the direction of each Force vectors, the magnitudes are the 3 unknowns.
Then, all of the Force vectors add up to a null vector. In other words, forces in each direction (i,j,k) add up to 0.
And by then you are left with 3 equations for 3 unknowns.