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Dot product question

  1. Jan 27, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm really at a loss here, if anyone could help me out I'd really appreciate it.


    Given 'a' and 'b' unit vectors,

    if |a+b| = root3, determine (2a-5b)dot(b+3a)
     
  2. jcsd
  3. Jan 28, 2009 #2

    Mark44

    Staff: Mentor

    |a + b|^2 = (a + b)[tex]\bullet[/tex](a + b)
    and |a + b| = sqrt(3) ==> |a + b|^2 = 3

    Now, use the fact that the dot product is associative, distributive, and commutative and the two equations above to see if you can evaluate (2a - 5b) )[tex]\bullet[/tex] (b + 3a).
     
  4. Jan 28, 2009 #3
    well I end up getting 13ab + 6a^2 - 5b^2

    The answer is -11/2

    I just can't seem to figure out how to get there :s
     
  5. Jan 28, 2009 #4

    Mark44

    Staff: Mentor

    Work with (a + b) [itex]\cdot [/itex] (a + b) = 3. You also know that a and b are unit vectors, which means that a [itex]\cdot [/itex] a = 1 and b [itex]\cdot [/itex] b = 1.
     
  6. Jan 28, 2009 #5
    Would I do like

    (a+b)dot(a+b)=3

    1 + 2ab + 1 = 3

    ab = 1/2

    then sub 1/2 into the ab and then get 6.5 + 6a^2 - 5b^2 and solve from there?
     
  7. Jan 28, 2009 #6

    Mark44

    Staff: Mentor

    Sort of, except that what you show as 6a^2 and -5b^2 is really 6a[itex] \cdot [/itex] a and -5b[itex] \cdot [/itex] b.
     
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