From what I understand, you are trying to sum vectors, and you are looking for a particular solution to get an end vector. In a way you are asking how to solve a problem that looks like this:
a1V1 + a2V2 + a3V3 + a4V4 = aV
where V are vectors, and a are magitudes. I am assuming that V are fixed (the way your plan jets are positioned?). I am also assuming that your vectors are 3 dimensional
So from the math alone, you have 3 dimensions and 4 parameters. Meaning that one of the 'a' can be anything. I don't think I can help any further than that without knowing the exact vectors.
In terms of code, solving for 'a's is trying to solve linear equations, typically done by using scipy's linalg:
https://docs.scipy.org/doc/scipy-0.15.1/reference/linalg.html
In particular, scipy.linalg.solve().
Again, you have to be very aware of the dimensions of the problem if you use the 4 vectors with the matrix, you will run into a lot of issues. Something must be done to determine one of the 'a' values before trying to solve the equations.
Edit: I thought a bit more about the problem, and I realized that there is a constraint in the system, and that is that the 'a's cannot be negative. So it seems like there are unique solutions to the system.