Vector proof thingy

I have always wanted to do math proof, but it is kind of hard XD . Now, I lately have been reading about vectors (yeah, i know, it is kind of nerdy, but school never teach me science well or what I want to learn well), and there is something called the cross product.

 uv                 

—-=cosθ

|u||v|

  

Vectors are basically arrows in a graph, and it is one method of multiplying them. I saw somewhere, though, that the distance between two vectors (makind a complete triangle) is equal to the law of cosines, and because of that, equation above is equal to law of cosines, since both equation should yield the same angle. So here is proof:

 

 

                

1. |v-u|^2=|u|^2+|v|^2-2|u||v|cosθ

 

2. |v-u|^2-|u|^2-|v|^2

———————– = cosθ

          -2|u||v|

 

3. v^2-2uv+u^2-v^2-u^2

—————————— = cosθ

           -2|u||v|

 

4.  -2uv

   ——- = cosθ

     -2|u||v|

 

5.  uv

    — = cosθ

    |u||v|           QED

                                            I hope I am not wrong.

 

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