Find Magnitude of Force F3 for Min Resultant FR

[quantum_enhan]

Homework Statement

Suppose we have the following forces:
F1=[5i]kN
F2=[-4j]kN
F3= unknown force 30 degrees from + y-axis.

How do you determine the magnitude of F3 such that the resultant FR for all three forces is a minimum?

Thanks in advance.

 

[kjohnson]

You know that the resultant 'r' of any given force broken down into x & y components is r=(x^2+y^2)^(1/2), but what is your total x & y component...
well its x=5kN+x' and y=-4kN+y' (where x' & y' represent the unknown components of F3)

From this you can get a relationship between x' & y' of F3 using the given angle..

With some algebra you will end up with something that is a function of F3, and how do you minimize a function?