Every vector field on $S^1$ is i-related to some vector field on $\mathbb{R}^2$, i is the inclusion map

Question

This question is from my quiz in Smooth manifolds and I am struck on this.

Question : Let $i: S^1 \to {\mathbb{R}}^2 $ be the usual inclusion map. Prove that every vector field on $S^1$ is i-related to some vector field on $\mathbb{R}^2$.

Let f be a smooth function from M and N where $X\in \mathfrak X(M)$ and $Y\in \mathfrak X(N)$. Then X and Y are f-related if $df_p (X_p)= Y_{f(p)}$.

For vector fields on Manifolds consider the definition here :https://en.wikipedia.org/wiki/Vector_field

Definitions are clear to me but I am not able to understand how to use them in this question maybe because so less examples have been solved in the class.

Can you give me a few hints? I would like to fully prove it by myself.

Thanks!