Distributive property of the cross product

jhsoccerodp@g
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Prove the following?

Vectors
(v-w)x(v+w)=2(vxw)
 
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Just use the distributive property of the cross product.
 


So I am guessing if you have VxV and WxW they are both equal to 0
 


Why do you have to guess that? What's the cross-product of two parallel vectors?
 


jhsoccerodp@g said:
So I am guessing if you have VxV and WxW they are both equal to 0
Yes.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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