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Math Help - Geometric interpetation of the addition of two dot products???

  1. #1
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    Geometric interpetation of the addition of two dot products???

    Hi,

    Let's assume that one needs to calculate the dot product between two 3 dimensional vectors (unit vectors) u_1 and u_2. This can otherwise be interpreted as finding the angle between them i.e. \cos\psi_m.

    Further assume that another pair of 3 dimensional unit vectors exists u_3 and u_2. Note that one of the unit vectors is the same in both cases. The dot product between these two can also be expressed by the angle between them as \cos\psi_n.

    What will be the result if I would like to add/substract these two angles \cos\psi_m +- \cos\psi_n?

    I would appreciate if someone could also explain me geometrically the implications of the addition/subtraction process. Is there any other way of expressing the result of the addition/substraction into a single term?

    Thanks a lot

    Regards

    Alex
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  2. #2
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    First, you need to be very sure that you understand that the dot product of two vectors is a number and not an angle. For unit vectors that number is the cosine of the angle between the vectors. If it is positive the angle is acute; if it is negative the angle is obtuse; if it is zero the angle is a right angle. As to you actual question, what does adding the cosines of any two angles with a common ray mean? Surely that are many different possible meanings.
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  3. #3
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    Yeap I do know that the dot product between two vectors is a scalar. Lets say that the vectors are not orthogonal so that the cosine is not zero. So does the addition of \cos\psi_nwith \cos\psi_m have a geometrical meaning?
    Can you please list some of those meanings?

    Thanks again

    Best Regards
    Last edited by tecne; November 10th 2007 at 10:30 AM.
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  4. #4
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    Quote Originally Posted by tecne View Post
    So does the addition of \cos\psi_nwith \cos\psi_m have a geometrical meaning?
    I have idea.
    What does 0.5 + 0.75 mean geometrically?
    What does 0.25 - 0.5 mean geometrically?
    What does cos(A)+cos(B) mean geometrically?
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