TS EAMCET · Maths · Three Dimensional Geometry
If \(\alpha\) is the angle between any two diagonals of a cube and \(\beta\) is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube then \(\cos \alpha+\cos ^2 \beta=\)
- A \(\frac{5}{9}\)
- B \(\frac{2}{9}\)
- C \(1\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\( \cos \alpha = \frac{(L,L,L) \cdot (-L,L,L)}{|(L,L,L)| |(-L,L,L)|} = \frac{L^2}{3L^2} = \frac{1}{3} \) \( \cos \beta = \frac{(L,L,L) \cdot (L,L,0)}{|(L,L,L)| |(L,L,0)|} = \frac{2L^2}{(L\sqrt{3})(L\sqrt{2})} = \frac{2}{\sqrt{6}} \)…
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