Answer
See answer below
Work Step by Step
We have vector space $R^2$.
Consider $R^2 \times R^2 \rightarrow R$ defined as $=v_1w_1-v_2w_2$ for all vectors $v=(v_1,v_2)\\
w=(w_1,w_2)$
Consider set $S=v \in R^2: v \ne 0, (v,v)=0$ with $v=(v_1,v_2) \in S$ we have:
$=(v_1)^2-(v_2)^2 \lt 0 \\
\rightarrow (v_1)^2\lt (v_2)^2\\
\rightarrow |v_1| \lt |v_2|$
We can notice that $v \in S, v_1 \ne 0$ and $v=(v_1,v_2) \in R^2$, thus:
$S=\{(v_1,v_2) \in R^2: |v_1| \lt |v_2|,v_1 \ne 0 \}$
