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Gamma angle

  1. Feb 24, 2009 #1
    For two arbitrary vectors in 3D space, subtending an angle, [tex] \gamma [/tex] , I know the cos relationship, but what's the sin relationship ? I ask because there is an ambiguity by only knowing the cosine form, since vector A can be either above or below vector B.

    [tex]
    cos\gamma = cos\theta_1 cos\theta_2 + sin\theta_1 sin\theta_2 cos( \phi_1 - \phi_2 )
    [/tex]

    Sorry I ask a stupid question in this forum, but I didn't know what's the correct term I should type in the search engine to search in the internet.
     
  2. jcsd
  3. Feb 24, 2009 #2

    Mark44

    Staff: Mentor

    I'm not sure I understand your question. Is there some reason you need to know which vector is above or below which? If you know the cosine of the angle between the two vectors--which you can get using the dot product: cos(gamma) = (A dot B)/(|A|*|B|)--the sign of cos(gamma) tells you whether gamma is in QI/QIV (cosine > 0) or in QII/QIII (cosine < 0).

    I'm not familiar with your formula. What do theta1, theta2, phi1, and phi2 represent?
     
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