Optimizing Cable Direction for Minimum Force in Vector Addition of Forces

[Suy]

Homework Statement

Three cables pull on the pipe such that they create a resultant force having magnitude FR. If two
of the cables are subjected to known forces, as shown in the figure, determine the direction θ of
the third cable so that the magnitude of force F in this cable is a minimum. All forces lie in the
x–y plane.What is the magnitude of F? Hint: First find the resultant of the two known forces.

Homework Equations

The Attempt at a Solution

I have the solution
but i don't understand "minimum" in this question?
"the third cable so that the magnitude of force F in this cable is a minimum. "

 

[JJBladester]

...determine the direction θ of the third cable so that the magnitude of force F in this cable is a minimum.

$$F_{R}=\left[1200sin45\textdegree+800cos30\textdegree\right]\hat{i}+\left[1200cos45\textdegree-800sin30\textdegree\right]\hat{j}$$

$$F_{R}=1541.35\hat{i}+448.53\hat{j}$$

$$\left|F_{R}\right|=1605.28$$

$$tan^{-1}\left (\frac{448.53}{1541.35}\right)=16.22\textdegree$$

Cheers!

 

[hafiy]

wat is the solution...can u give me?