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The main object of this paper is to determine the maximum number of $\{0,\pm1\}$-vectors subject to the following condition. All vectors have length $n$,exactly $k$ of the coordinates are $+1$ and one is $-1$, $n \geq 2k$. Moreover,there are no two vectors whose scalar product equals the possible minimum,$-2$. Thus, this problem may be seen as an extension of the classical Erd\Hos-Ko-Rado theorem. Rather surprisingly there is a phase transition in thebehaviour of the maximum at $n=k^2$. Nevertheless, our solution is complete.The main tools are from extremal set theory and some of them might be ofindependent interest.

Erd\H os-Ko-Rado theorem for $\{0,\pm 1\}$-vectors