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Given vectors how to find third equation

  1. Jun 2, 2014 #1
    1. The problem statement, all variables and given/known data

    If |v|=4, |w|=3 and the angle between and is pi/3, find |2v −w|

    2. Relevant equations
    ##cosθ=\frac {v dot w} {|v||w|} ##


    3. The attempt at a solution
    ## 6= v dot w ##

    This is as far as I got. How would I find the separate values of v and w for the equation?
     
  2. jcsd
  3. Jun 2, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    Very good! How is the absolute value of a vector defined with dot product by itself?
    You do not need to know the individual vectors. You need the absolute value of 2v-w.

    ehild
     
  4. Jun 2, 2014 #3
    u dot u = ##|u|^2## so |u|= ##\sqrt {u dot u} ## ?

    Possibly, that becomes |2v-w|=sqrt(something?) or would |?|(1/2)=|2v-w|

    I'm afraid I don't see how things are connecting to the third equation though.

    1/2 = (something analogous to u dot v)/|2v-w|?
     
    Last edited: Jun 2, 2014
  5. Jun 2, 2014 #4

    DrClaude

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    Staff: Mentor

    Start from that definition. What then is ##\sqrt{(2v-w) \cdot (2v-w)}##?
     
  6. Jun 2, 2014 #5
    Got it, thanks.
     
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