Five distinct unit vectors v₁,…,v₅ in ℝ⁷ have nonpositive integer pairwise inner products for unequal indices. N counts ordered pairs (r,s), including r=s, with nonzero inner product. Find the largest N.
Cauchy–Schwarz restricts off-diagonal products to 0 or −1. Value −1 means the vectors are opposites, and a given distinct vector has at most one opposite. Five vectors allow at most two opposite pairs, contributing four ordered off-diagonal pairs, plus five diagonal ones: 9. Example {e₁,−e₁,e₂,−e₂,e₃} attains it. **A**.
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