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

[SAHM1500]

Homework Statement

4. Prove that



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

Homework Equations

The Attempt at a Solution

I do know how can I start. i feel confuse! please help me

 

[SammyS]

Homework Statement

4. Prove that

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

Homework Equations

The Attempt at a Solution

I do know how can I start. i feel confuse! please help me

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:

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

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

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