Vectors Math Help (solution check)

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Homework Statement


Use three specific vectors in 3 space to show that ⃗ a ×(b⃗ ×c⃗ ) ≠ (a⃗ ×b⃗ )×c⃗

solution is in pdf...

Homework Equations

The Attempt at a Solution

 

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amy098yay said:

Homework Statement


Use three specific vectors in 3 space to show that ⃗ a ×(b⃗ ×c⃗ ) ≠ (a⃗ ×b⃗ )×c⃗

solution is in pdf...

Homework Equations

The Attempt at a Solution

Looks good now.
For future reference, you can check your answers. a x (b x c) should be perpendicular to both a and a x c. Just calculate the dot product of a and a x (b x c), and of (b x c) and a x (b x c). Each dot product should be zero. Same thing with the other triple product.
 
for sure, thank you so much for taking time out of your day to help me with this problem :)
 
You're welcome! Most of us helping out here like to do this...
 
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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