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Math Help - Trigonometry and Miller indices.

  1. #1
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    Trigonometry and Miller indices.

    One way to prove the distance between two planes is to use the equation Cos(alpha_1)^2 + Cos(alpha_2)^2 + Cos(alpha_3)^2 = 1. In this equation Cos(alpha) is the angle between the normal to the plane and the (x,y,or z axis).

    My main question is why is this equation (Cos(alpha_1)^2 + Cos(alpha_2)^2 + Cos(alpha_3)^2 = 1) true?

    Thanks in advance.

    I have attached a figure to illustrate the problem more clearly.

    Trigonometry and Miller indices.-plane.png
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  2. #2
    MHF Contributor
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    If \alpha is the angle between a unit vector and a coordinate axis, then \cos\alpha is the projection of that vector to that axis. Then Pythagoras theorem can be used to prove that the sum of squares of the coordinates of a unit vector is 1.
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