Ok, basically what I did so far is to draw the vectors from the origin of both the velocity and the first force.
For the velocity, I made a vector(?) with a slope of (-4/3) and a magnitude of 5.
For the first force, I made a vector(?) with a slope of (-3) and a magnitude of (40)^(1/2).
Now for finding the second force, I simply "added" (4N)i - (2N)j in order to reach the velocity vector(?), but the magnitude had to be multiplied with a scalar(?) of two.
Sorry, I'm a little confused with vector definitions, I hope I got them right and what I wrote made sense. My question now is did I reach the answer or is this completely wrong? If so, how can i put this into mathematical form, instead of simply ploting vectors on a graph?

The way I read this (unusual!) problem, the answer is quite simple. Maybe I misunderstand the problem, though.
The particle seems to be moving at constant velocity, right ?
So what's the total force on the particle then ?

Well if there's no acceleration, then there is no force. But I don't think continuously here means that the particle is at a constant velocity. Afterall, the problem indicates that there are two existing forces.

wait... ok, if continously here means constant velocity, then the answer is the opposite vector of (-2N) i + (6N) j to achieve translatoral equilibrium. So does continuously in the problem here mean constant velocity?

As I said, I find the problem wording rather strange. But I don't see any other option, given that if you do NOT assume constant velocity, there's nothing in the description that would hint of an acceleration from which you can calculate the force. The velocity at the initial moment is useless to calculate it.
So if we do some "psychology of the one who asks the question" what could be his aim ? I think his aim is to see whether you've understood that something with constant velocity doesn't have any TOTAL force applied to it (Newton's second law!). This is an important concept. For instance, an airplane flying at constant velocity has several forces acting upon it: wing lift, motor thrust, air resistance, gravity. But the TOTAL force is zero. In order to "confuse" you he gave a vector that doesn't have anything to do with it.
But the wording "continuously" is a bit disturbing. He should have said "constant".