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Angle between two vectors given their scalar product and magnitude of their vector pr

  1. Aug 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Vectors and have scalar product -7.00 and their vector product has magnitude 3.00.
    What is the angle between these two vectors?

    2. Relevant equations

    |A| |B| cosθ = -7
    |A| |B| sinθ = 3

    3. The attempt at a solution

    tanθ = (-3/7)
    tan-1(-3/7)=θ

    When I enter tan-1(-3/7) into my calculator, I get -23.199, but when I enter 23.199 into MasteringPhysics, it tells me that I am incorrect. What am I doing wrong?

    Thanks!
     
  2. jcsd
  3. Aug 30, 2012 #2
    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    Is the angle expected in degrees or radians?
     
  4. Aug 30, 2012 #3
    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    The answer is required to be in degrees.
     
  5. Aug 30, 2012 #4
    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    What is the range of arctan? From the given values, can you determine whether the angle is really in that range?
     
  6. Aug 30, 2012 #5
    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    I believe that the range of arctan is 270°<θ<90°. Correct? 23.199° seems to be in that range…

    Thanks for the help. It's been a while since I've done this stuff.
     
  7. Aug 30, 2012 #6

    CAF123

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    Gold Member

    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    The range given does not make sense. The range should be (-π/2,π/2).
     
  8. Aug 30, 2012 #7
  9. Aug 30, 2012 #8
    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    I guess it would actually lie in quadrant II whereas the range of arctan is quadrants I and IV. So what should I do?
     
  10. Aug 30, 2012 #9
    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    You should express you angle via some auxiliary angle that is in the range of arctan, obtain the value of the auxiliary angle, and then get your angle.
     
  11. Aug 30, 2012 #10

    gabbagabbahey

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    Homework Helper
    Gold Member

    Re: Angle between two vectors given their scalar product and magnitude of their vecto

    You should take care to notice two things here:

    (1) If |A| |B| cosθ = -7, then cosθ must be negative. In which quadrants is cosθ negative?

    (2) tanθ has a period of ∏ radians, so tanθ = tan(θ+n∏) for any integer n, and tan-1(tanθ) = θ +n∏. Can you find a value of n that gives you an angle in the correct quadrant for θ +n∏=tan-1(-3/7)?
     
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