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
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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