Linear independence of isotropic vectors relative to a bilinear form.

Question

Let $V$ be a vector space over $\mathbb{F}$, and let $g: V\times V\to \mathbb{F}$ be a bilinear form. A vector $v\in V$ is isotropic if $g(v,v) = 0$. Let $v,w\in V$ be 2 isotropic vectors such that $g(v,w)=0$. Under what conditions are they independent? If they weren't isotropic (or at least one of them is sufficient), then the proof is like of 2 orthogonal vectors in an inner product space.