Given one cross product, find another cross product

Colts
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Homework Statement


Calculate the cross product assuming that u X w = <-7,1,8>
Find (-3u + 4w) X w = ?


Homework Equations


I'm not sure. I know you have to relate the cross product to something inorder to find what u and w are, but don't know what equations to use.


The Attempt at a Solution


Don't know where to start
 
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I think it is best if you use these 3 characteristics.
1. u x w = u w sin(theta)
2. λu x w = λ (u x w)
3. (u + v) x w= u x w + v x w
 

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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