Çözüldü Object Diagonal of Rectangular Prism - Trigonometry

What is the sum of the squares of the cosines of the angles formed by an object diagonal (connecting two opposite vertices) and three edges of a rectangular prism?

A) 1 / 2
B) 1
C) 3 / 2
D) 2
E) 5 / 2


https://i72.servimg.com/u/f72/19/97/10/39/rectan11.png

[AB] ⊥ [BC']
[AA'] ⊥ [A'C']
[AD] ⊥ [C'D]
∡BAC' = x
∡C'AD = y
∡A'AC' = z
cos(x) = a / k, cos(y) = b / k, cos(z) = c / k
[ cos(x) ]^2 + [ cos(y) ]^2 + [ cos(z) ]^2 = (a^2 + b^2 + c^2) / k^2 = k^2 / k^2 = 1.

Source: "Space Geometry and Trigonometry Problems with Solutions", Vol.2, Tahsin Çizenel, 1968, Pages 11 and 26, Question 15