Let (B_{t}=left(b_{t}, beta_{t}ight), t geqslant 0), be a two-dimensional Brownian motion and (alpha in[0,2 pi)). Show that

Question:

Let $B_{t}=\left(b_{t}, \beta_{t}ight), t \geqslant 0$, be a two-dimensional Brownian motion and $\alpha \in[0,2 \pi)$. Show that $W_{t}=\left(b_{t} \cdot \cos \alpha+\beta_{t} \cdot \sin \alpha, \beta_{t} \cdot \cos \alpha-b_{t} \cdot \sin \alphaight)^{\top}$ is a two-dimensional Brownian motion. Find a suitable $d$-dimensional generalization of this observation.

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