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Homework Help: How to find a vector that has the same direction

  1. Nov 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Can anyone help me with his problem:
    how to find a vector that has the same direction as <-2,4,2> but has length 6


    2. Relevant equations



    3. The attempt at a solution
    the length of that vector is: 6= (-2)^2*a^2+(4)^2*b^2+(2)^2*c^2
    Then I don't know what to do next?
     
  2. jcsd
  3. Nov 4, 2007 #2
    Suppose I have a unit vector (a,b,c). What is the length of k(a,b,c)?
     
  4. Nov 4, 2007 #3
    divide the lengh from the original vector, that will give you the unit vector. What do you do with the unit vector to get a lengh of 6 and same direction?
     
  5. Nov 4, 2007 #4
    k(a,b,c)=(ka,kb,kc)=(-2k,4k,2k)
    lenght= root(4k^2+16k^2+4k^2)=6
    => root( 24k^2) =6
    => k*root(24)=6
    =>k= 6/root(24)= 3/root6
    oh I got it, Thank you very much!! Ziox AND Antineutron
     
  6. Nov 4, 2007 #5
    Although you haven't done what we said, that works. Note how this scaling quantity is unique up to +/-. Which makes sense: the direction induced by (-2,4,2) is just a line in R^3.

    The scaling value that you actually calculated is the ratio of new length to the original length - dividing by the old and multiplying by the new.
     
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