A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option

  • A

    $\vec r.\vec \tau  > 0$ and $\vec F.\vec \tau  < 0$

  • B

    $\vec r.\vec \tau  = 0$ and $\vec F.\vec \tau  = 0$

  • C

    $\vec r.\vec \tau  = 0$ and $\vec F.\vec \tau  \ne 0$

  • D

    $\vec r.\vec \tau  \ne 0$ and $\vec F.\vec \tau  = 0$

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