Question on vertical pole and equilibrium

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To solve the problem of finding the tensions in the other two cables attached to a vertically balanced pole, the equilibrium condition must be applied, ensuring that the sum of the x and y components of all forces equals zero. Given that one cable has a tension of 6000 Newtons, the components of this force must be calculated using the provided unit vectors. The tensions in the other two cables can then be expressed in terms of their components, which should also balance out to maintain equilibrium. The approach of setting the components of the other two ropes equal to those of the 6000N rope is correct, but additional calculations are needed to ensure all forces are accounted for. Ultimately, the correct setup of equations will lead to determining the unknown tensions.
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I have this problem where a pole is vertically balanced, and there are three wires attach on top of it. The wires are fasten to the ground. It looks like a three side pyramid. The question tells me that one of the cable has a tension of 6000 Newtons. How can I find the tension on the other two cable? The wires are not equally distanced. All the lengths are given as well, and I know the unit vectors too.
 

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You need to calculate the components for each force vector (which are directed along the wires). To be in equilibrium the x and y components much each sum to 0.
 
How would I set up the equation with the 6000N?
 
I thought about it. After find the xyz components for the 6000N rope, I made the xyz components of the other two ropes equal to it. Is this the right approach?
 
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