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Unknown angle between two vectors

  1. Jan 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Scalar product of vectors AB = -6; vector product of AB = 9. Find the angle between vectors A and B.


    2. Relevant equations
    Scalar product: cos(θ)*AB
    Vector product: sin(θ)*AB
    (sin(θ))/cos(θ) = tanθ

    3. The attempt at a solution
    AB = -6/cos(θ)
    AB = 9/sin(θ)
    9/sin(θ) = -6/cos(θ)
    9/-6 = (sin(θ))/cos(θ)
    3/-2 = tan(θ)
    tan^-1(3/-2) = -56° which I take to mean 56° from each other.
    But their answer is 124° which is -56° + 180°. How can this be when the whole time we are dealing with one angle between two vectors?
     
  2. jcsd
  3. Jan 8, 2013 #2
    tan θ = negative value means θ can only be 90<θ<180 or 270<θ<360.


    I have a question also , why the vector product which is a vector can equal to 9? is that a magnitude of AxB?
    Thank you
     
  4. Jan 8, 2013 #3
    Ohhhh, I see, thanks.

    Yes, I should have mentioned that.
     
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