Minkowski space/Form is 1/Restriction to observer space/Exercise

Let ${}V$ be a Minkowski space of dimension ${}n$. We consider the set

${}T={\left\{v\in V\mid \left\langle v,v\right\rangle =1\right\}}\,.$

Let ${}w$ be the observer vector of an observer ${}B$, and let ${}V_{B}$ denote his space component. What is the shape of ${}T\cap V_{B}$?

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