Suppose $(\pi,E,M)$ is a vector bundle (total space $E$, base space $M$) and that $S \subset M$ is an embedded submanifold. If $E$ has positive rank, show that every smooth section of $E|_S$ (the vector bundle restricted to $S$) extends smoothly to all of $M$ $\iff$ $S$ is properly embedded.
So I'm trying to work this out and I'm not having much luck getting started. How is the fact that the embedding is proper going to help me out? Thanks