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In this paper, we investigate Erd\H os--Ko--Rado type theorems for familiesof vectors from $\{0,\pm 1\}^n$ with fixed numbers of $+1$'s and $-1$'s. Scalarproduct plays the role of intersection size. In particular, we sharpen ourearlier result on the largest size of a family of such vectors that avoids thesmallest possible scalar product. We also obtain an exact result for thelargest size of a family with no negative scalar products.

Intersection theorems for $(-1,0,1)$-vectors