Prove thath if v, w, and x are in R2 or R3 an v is orthogonal to both w and x, then v is orthogonal to every vector span in {w, x}.

I'm totally lost on this problem. So far what I've got is that

v . w = 0

v . x = 0

v1w1 + .... + vnwn = 0

v1x1 + .... + vnxn = 0

v1x1 + .... + v1x1 = v1w1 + .... + vnwn

v1(x1 - w1) + .... + vn (xn - wn) = 0

(I'm not even sure if this part is useful or not)

Let's say there is a y that is a vector in the span of {w, x}. How would I prove that v . y = 0?

Thanks