Reflecting a vector $k_1$ at a plane with normal vector $\hat{n}$ is described by:
$$ \hat{k}_2 = \hat{k}_1 - 2(\hat{k}_1 \cdot \hat{n})\hat{n}$$
With $k_2$ being the reflected vector. All three vectors are normalised and 3 dimensional.
How can you resolve this equation to $\hat{n}$?
In words: "For which normal vector does a given $k_1$ result in a given $k_2$?"