We return to the case where $\mathbb { K }$ is an arbitrary field of characteristic zero. Let $\left( V _ { i } \right) _ { 1 \leq i \leq 3 }$ be three $\mathbb { K }$-vector spaces of finite dimension and $q _ { i } \in \mathcal { Q } \left( V _ { i } \right)$ for $1 \leq i \leq 3$ satisfying $q _ { 1 } \perp q _ { 3 } \cong q _ { 2 } \perp q _ { 3 }$. Show that $q _ { 1 } \cong q _ { 2 }$.
Hint: one may reason by induction and use questions 17 and 18.