Q78Section C (Part C)78 of 120

Isotropic vector of a nondegenerate form on $\mathbb R^2$

Let $B(v,w)$ be a nondegenerate symmetric bilinear form on $\mathbb R^2$ and let $q(v)=B(v,v)$ be the corresponding quadratic form. Suppose there exist vectors $v,w\in\mathbb R^2$ such that $B(v,v)=0$ and $B(v,w)\neq0$ . Which of the following statements are necessarily true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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