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

1. Jan 20, 2012

SAHM1500

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

2. Jan 20, 2012

SammyS

Staff Emeritus
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 $\displaystyle \frac{d}{dt}\left( \vec{r}\cdot\vec{v}\times\vec{a} \right)=\vec{r}\cdot\vec{v}\times\dot{\vec{a}}\ ?$

If so use the product rule.

Also the following:
$\displaystyle \frac{d\vec{r}}{dt}=\dot{\vec{r}}=\vec{v}$

$\displaystyle \frac{d\vec{v}}{dt}=\dot{\vec{v}}=\vec{a}$

$\displaystyle \frac{d\vec{a}}{dt}=\dot{\vec{a}}$​