# 3d coordinate angles α β γ

1. Feb 8, 2014

### Tiven white

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. Feb 9, 2014

### voko

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?