Finding Relations for Net Force with Two Exerted Forces at 150 Degrees Angle

[Nanoath]

Homework Statement

The directions of two forces $$\vec{F_{1}}$$ and $$\vec{F_{2}}$$ (with F1 > F2) that are exerted at a point from angle of 150 degrees between them. Find the relations that must exist between the magnitudes of these forces $$\vec{F_{1}}$$ and $$\vec{F_{2}}$$ so that the net force has a magnitude equal to that of $$\vec{F_{1}}$$ .

Homework Equations

$$\sum\vec{F}=0$$

The Attempt at a Solution

none so far.
-----------
Need help getting started..
-----------
$$\vec{F_{1}}$$ = $$\vec{F_{1}}$$ + $$\vec{F_{2}}$$ I think this is what the problem is stating, but wouldn't that mean F2 = 0?

 

[Dschumanji]

Start out by setting up a coordinate system to place the vectors in so you can analyze them in terms of components. To simplify things, try directing F₁ along the positive x axis.

To find the net force vector just add the components. Use the pythagorean theorem to find the magnitude of the net force vector. You want the magnitude of that force to equal the magnitude F₁.

The only "problem" I seem to run into with this question is that I'm not sure the inequality you introduced in the problem statement is a constraint that must always be satisfied. If that is the case, there is only one answer and your guess is correct, but not for the reasons I think you are thinking.