Question 158
Let $O$ be an interior point of the triangle $ABC$. Prove that there exist positive integers $p, q$ and $r$, such that
$$
|p \cdot \vec{OA} + q \cdot \vec{OB} + r \cdot \vec{OC}| \lt \frac{1}{2007}.
$$
$$
|p \cdot \vec{OA} + q \cdot \vec{OB} + r \cdot \vec{OC}| \lt \frac{1}{2007}.
$$