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#### Dhamnekar Winod

##### Active member

- Nov 17, 2018

- 103

$$\frac{d}{dt}(r \times (v\times r))=||r||^2 *a+ (r\cdot v)*v-(||v||^2+ r\cdot a)*r \tag{1}$$

Where

**r(t)**is a position vector

**(x(t),y(t),z(t)),**$v(t)=\frac{dr}{dt}=(x'(t),y'(t),z'(t)), a(t)=\frac{dv}{dt}=\frac{d^2r}{dt^2}=(x''(t),y''(t),z''(t))$ Note: v=velocity, a= acceleration

My attempt:-

I know $\frac{d}{dt}(f\times g)=\frac{df}{dt}\times g +f\times \frac{dg}{dt}$. I also know for any vectors

**u, v, w**in $\mathbb{R^3}, u\times (v\times w)=(u\cdot w)*v-(u\cdot v)*w $

But I don't understand how to use these formulas to prove

**equation (1)**?

If any member knows answer to this question may reply with correct answer.