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[QUE/CM-04018]

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\(\newcommand{\PB}[1]{[#1]_\text{PB}}\)  Show that the Poisson brackets of components of angular momentum  \(\vec{L}\)
with the following quantities vanishes.

  1. \(\vec{r}\cdot\vec{p}\)
  2. \(\vec{r}\cdot\vec{L}\)
  3. \(\vec{L}\cdot\vec{p}\)
  4. \( \vec{L}^{\,2}\)

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