AP EAMCET · Maths · Three Dimensional Geometry
The angle between any two diagonals of a cube is
- A \(\cos ^{-1}\left(\frac{1}{3}\right)\)
- B \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
- C \(\cos ^{-1}\left(\frac{1}{2}\right)\)
- D \(\cos ^{-1}\left(\frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(\cos ^{-1}\left(\frac{1}{3}\right)\)
Step-by-step Solution
Detailed explanation
Diagonal of cube \(\mathbf{O P}\) and \(\mathbf{A Q}\). \[ \begin{aligned} & \mathbf{O P}=a \hat{\mathbf{i}}+a \hat{\mathbf{j}}+a \hat{\mathbf{k}} \\ & \mathbf{A Q}=-a \hat{\mathbf{i}}+a \hat{\mathbf{j}}+a \hat{\mathbf{k}} \end{aligned} \] Angle between diagonal i.e.…
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