GATE CSE 2021 Set 2 Q47: Maximum number of mutually orthogonal non-zero vectors in R^10

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 $\mathcal{L}$?