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Cross product and Dot product problem

  1. Sep 18, 2013 #1
    1. The problem statement, all variables and given/known data

    if v x w = <5,5,-2>
    (v cross w)

    and

    v * w = 6
    (v dot w)

    then what is the tan(θ) between the two vectors v and w?


    3. The attempt at a solution

    well I was thinking v x w = |v||w|sinθ
    as well as v dot w (v*w) = |v|w|cosθ

    divide one equation by the other and the absolute values on the right cancel out,
    but then you get a vector divided by a number on the left side equals tanθ

    is this how you do this problem?
     
  2. jcsd
  3. Sep 18, 2013 #2
    You have a problem with the first equation in your attempt at solution. It should read:
    |v × w| = |v| |w| sinθ

    You are right that v × w is a vector, and the correct equation for it would be:
    v × w = |v| |w| sinθ n
    where n is the unit vector perpendicular to both v and w given by the right-hand rule.
     
  4. Sep 18, 2013 #3

    Mark44

    Staff: Mentor

    To expand on what Jolb said, since you're given that v x w = <5, 5, -2>, you have enough information to find |v x w|.
     
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