What additional force is needed to keep the object at rest?

[ArcadeEdge]

This is a problem from my Calculus class in the sections about vectors.

Homework Statement

Two forces F1 = 2i + 6j and F2 = 2i -2j act on an object. What additional force is needed to keep the object at rest?

Homework Equations

I'm not sure where to start.

The Attempt at a Solution

I know for the body to be at rest it has to equal 0.
I've tried finding the displacement between the two given vectors which gives me <0, 81>. I'm not sure if that is even relevant. The only thing I really get right now is that something has to equal zero. I feel like this is an easy problem but I don't know where to get started..

thanks in advance.

 

[nonequilibrium]

So we're looking for the third force F3, correct? Let's write it out as F3 = x i + y j + z k where x, y and z are unknown at this moment. (I'm assuming you're working in three dimensions, if you're only working in two, forget the "z k" term)

Now think about what the 'only thing you really get right now' tells you about the relation between these three forces...

 

[ArcadeEdge]

You add them together and set them equal to zero and solve for xi and yj right? When I do that I get 0 for both x and y.

 

[nonequilibrium]

The technique sounds right, I'm guessing you're making a math mistake

can you type it out?