For two $n$-dimensional real vectors $P$ and $Q$, the operation $s(P, Q)$ is defined as follows: $$s(P, Q) = \sum_{i=1}^n (P[i] \cdot Q[i])$$ Let $\mathcal{L}$ be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors $P, Q \in \mathcal{L}$, $s(P, Q) = 0$. What is the maximum cardinality possible for the set $\mathcal{L}$?

For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows: s(P, Q) = i=1n (P[i] Q[i]) Let L be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P, Q L, s(P, Q) = 0. What is the maximum cardinality possible for the set L?

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