How can I find the length of this pole?

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SUMMARY

The discussion focuses on calculating the length of a pole BC supported by a cable AB, given a force of 70 lb applied at point B and a moment of -763 lb ft about the x-axis. The user attempts to relate the torque to the pole length using vectors but struggles with the definitions and calculations. Key equations include τ = r × F and τ = T1 + T2, which are essential for solving the problem. The user is advised to clarify the vectors involved, particularly the force direction and the position vector OB.

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GaussianSurface

Homework Statement


A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght.
I'LL ATTACH AN IMAGE SO YOU CAN SEE IT.

Homework Equations


τ= torque or moment of force
τ= r X F
Tτ= T1+T2
Tτ=(r1 + r2) x F

The Attempt at a Solution


I don't know how to compute the lenght, I was thinking about it maybe was related with the torque or moment of force (let me know if this is true).
What I tried to do was this:
r1= 4i + 6k
e= 4i+6k
e=√4^2+6^2
e=√52
e=4/√52 + 6/√52

F= 70(4/√52 + 6/√52) = 38.82i+58.24k
and by performing the determinant

τ= -0.04 lb/ft
So far I should've got the T1 and now I'd do the same but this time with other vectors ⇒ 4i-6k

I don't think it's correct since I got a result on differents units that don't measure the lenght. PLEASE TRY TO TELL WHAT I'M WRONG AND WHAT I'M RIGHT.
 

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GaussianSurface said:
r1= 4i + 6k
How are you defining r1? That does not look like a useful vector.
The force is directed along BA. Can you write down that vector?
The point of application of the force is B, so you also need the vector OB. Can you write that down?
 

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