Vector Calculations | Find ⎮v-2w⎮

MozAngeles
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Homework Statement



If ⎮v⎮=2, ⎮w⎮=3, and the angle between v and w is \pi/3[\tex], find ⎮v-2w⎮.<br /> <br /> <h2>Homework Equations</h2><br /> <br /> Im not sure how to go about this. maybe use \cos\theta[\tex]=u∙v/⎮u⎮⎮v⎮&lt;br /&gt; &lt;br /&gt; &lt;h2&gt;The Attempt at a Solution&lt;/h2&gt;&lt;br /&gt; i&amp;#039;m not sure where to start. i know this has to be pretty straightforward, but i don&amp;#039;t see it...&lt;br /&gt; anyt help would be nice thanks.
 
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Hi MozAngeles! :smile:

(write /tex not \tex :wink:)

hint: |v - 2w|2 = (v - 2w).(v - 2w) :wink:
 
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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