$Sp(V)$ acts transitively on $V^*-\{0\}$ where $\Omega$ here is symplectic 2 form

Question

Let $\dim(V)=6$. Show that $Sp(V,\Omega)$ acts transitively on $V^*-\{0\}$, where $\Omega$ here is a symplectic 2 form on $V$. ($V^*$ here is algebraic dual of $V$)

Answer 1

Hint. Show first that any non-zero vector is part of a symplectic basis.