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Prove thatd d/dt[ r · ( v × a ) ] = r · ( v × a ̇ )

  1. Jan 20, 2012 #1
    1. The problem statement, all variables and given/known data
    4. Prove that

    Prove thatd d/dt[ r · ( v × a ) ] = r · ( v × a ̇ )

    2. Relevant equations

    3. The attempt at a solution
    I do know how can I start. i feel confuse!! please help me
  2. jcsd
  3. Jan 20, 2012 #2


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    Re: Prove

    Hello SAHM1500. Welcome to PF !

    Is that supposed to be " a dot ", i.e. the derivative of acceleration with respect to time?

    Are you to prove that [itex]\displaystyle \frac{d}{dt}\left( \vec{r}\cdot\vec{v}\times\vec{a} \right)=\vec{r}\cdot\vec{v}\times\dot{\vec{a}}\ ?[/itex]

    If so use the product rule.

    Also the following:
    [itex]\displaystyle \frac{d\vec{r}}{dt}=\dot{\vec{r}}=\vec{v}[/itex]

    [itex]\displaystyle \frac{d\vec{v}}{dt}=\dot{\vec{v}}=\vec{a}[/itex]

    [itex]\displaystyle \frac{d\vec{a}}{dt}=\dot{\vec{a}}[/itex]​
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