Cross Product Proof: u X v X w = u X (v X w)

MJC684
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Homework Statement



(u X v) X w = u X (v X w) Iff (u X w) X v = 0

Homework Equations



(u X v) = -(v X u)

The Attempt at a Solution



I know that I am supposed to prove this by proving P --> Q and Q --> P
I know that if (u X w) X V = 0 then (u X w) is a scalar multiple of v.

How do i deduce Q from P and P from Q?
 
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Hi MJC684! :smile:

What is (u X v) X w - u X (v X w) ? :wink:

(use the Einstein summation convention if you know it, otherwise use coordinates)
 

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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