# Zero sections of any smooth vector bundle is smooth?

Could any one give me hint how to show that the zero section of any smooth vector bundle is smooth?

Zero section is a map $\xi:M\rightarrow E$ defined by $$\xi(p)=0\qquad\forall p\in M.$$

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Smoothness can be checked locally on $M$ and locally $E$ is trivial.
@KutukKatuk If $M$ and $N$ are smooth manifolds and $p\in N$, then the inclusion $M\to M\times N$ given by the rule $m\to (m,p)$ is smooth. If you understand this and combine it with Mariano's answer, then you will have found an answer to your original question. –  Amitesh Datta Aug 8 '12 at 0:32