I'm trying to find an algorithm that will use any combination of a given set of operators on a given set of vectors to reach a target vector. At all costs I want to avoid using brute force, I believe this problem has an elegant solution.

**Example problem:**  

Given the vectors `V1 = [0, -1]`; `V2 = [2, 1]`; `V3 = [-1, 0]`;  

And the operators `L1` and `L2`. Who behave like `L1[V1, V2] = V1 + V2`; `L2[V1, V2] = V1/V2`  

Try to reach the target vector `T = [-0.5, 0]`

**Solution:**  

`L1[V1, V2] = [0, -1] + [2, 1] = [2, 0]`  

`L2[V3, L1[V1, V2]] = [-1, 0] / [2, 0] = [-0.5, 0]` (0/0 division was pointed out to me, which was a mistake; but I think what the solution is trying to accomplish still makes sense)

**What I've Tried:**  

I have tried treating this question as a `vector combination problem`, but I haven't figured out how to introduce a list of operators. Please let me know if my terminology is incorrect or confusing; any help is appreciated.