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Homework Help: Scalar projection of b onto a (vectors)

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data

    If a = <3,0,-1> find the vector b such that compaB = 2

    2. Relevant equations


    3. The attempt at a solution

    [tex]|a| =\sqrt{3^2 + 1^2} = \sqrt{10}[/tex]

    compaB = [tex]\frac{ a\cdot b}{|a|}[/tex]

    [tex]2 = \frac{3(b1) - 1(b3)}{\sqrt{10}}[/tex]

    [tex]2\sqrt{10} = 3(b1) - 1(b3)[/tex]

    I dont know what to do from here
  2. jcsd
  3. Sep 9, 2010 #2


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    Homework Helper

    You said, find the vector b whose projection on a is twice as long as a itself, but of course there are infinitely many such vectors. What you have shown here is that there is that a vector of the form b = (r, s, 3r - 2√10) for any real numbers r and s satisfies compab = 2.
  4. Sep 9, 2010 #3
    Sorry but I dont understand.
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