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3d coordinate angles α β γ

  1. Feb 8, 2014 #1
    1. The problem statement, all variables and given/known data[/
    In 3-D coordinate space, any two of the coordinate angles must …
    Select one:
    a. sum to less than 1
    b. be greater than 90° but less than 180°
    c. each be greater than 45°
    d. sum to greater than 90° (if they are both less than 90°).
    e. have cosines less than (√2/2).

    2. Relevant equations

    (cosα(α))^2 + (cos(β))^2 + (cos(γ))^2 = 1

    3. The attempt at a solution.

    since the sum of the squared cosine of alpha beta and gamma = 1 the answer to me is e reason being if the value of the cosine of the angle is (√2/2) then the square = 0.5 and the sum of two of these angles = 1 therefore the cosine has to be less than (√2/2). c could also be an option since all angles with (√2/2) is greater than 45°. but when i tried with example 150° for both angles the cosine is > than (√2/2) but negative. but when squared it is positive which implies the sum of the two would be greater than 1 and denounces 'c' is 'e' then the required solution.
     
  2. jcsd
  3. Feb 9, 2014 #2
    Consider a simple vector given by cosines (1, 0, 0). This is simply a unit vector directed along the X axis. Is either C or E true for it?
     
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