ISL 1989 Problem 57

Let $v_1, v_2, \ldots, v_{1989}$ be a set of coplanar vectors with $|v_r| \leq 1$ for $1 \leq r \leq 1989.$ Show that it is possible to find $\epsilon_r$ , $1 \leq r \leq 1989,$ each equal to $\pm 1,$ such that $$\left | \sum^{1989}_{r=1} \epsilon_r v_r \right | \leq \sqrt{3}.$$