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Math Help - Dot Product problem!!!

  1. #1
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    Dot Product problem!!!

    Hi all,

    I have 3 pairs of 3-dimensional unit vectors. I take the dot product of those pairs of vectors and so I obtain the angle between them. In other words I can express the three dot products by their respective angle \cos\theta_1, \cos\theta_2 and \cos\theta_3. I was wondering if there is any interesting geometric interpretation by the addition of those three angles \cos\theta_1 + \cos\theta_2 + \cos\theta_3?

    I am trying to find a way of simplifying/re-writing the above addition of angles and hence express it as a single term.

    I would appreciate anyones help

    Regards

    Alex
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  2. #2
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    Quote Originally Posted by tecne View Post
    Hi all,

    I have 3 pairs of 3-dimensional unit vectors. I take the dot product of those pairs of vectors and so I obtain the angle between them. In other words I can express the three dot products by their respective angle \cos\theta_1, \cos\theta_2 and \cos\theta_3. I was wondering if there is any interesting geometric interpretation by the addition of those three angles \cos\theta_1 + \cos\theta_2 + \cos\theta_3?

    I am trying to find a way of simplifying/re-writing the above addition of angles and hence express it as a single term.

    I would appreciate anyones help

    Regards

    Alex
    I don't know about the sums of the cosines, but in general
    cos^2(\theta _1) + cos^2(\theta _2) + cos^2(\theta _2) = 1

    -Dan
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