Question

The angle between any two diagonal of a cube is

• A. $45^{\circ }$
• B. $60^{\circ }$
• C. $30^{\circ }$
• D. ${\tan }^{-1}(2\sqrt{2})$

Answer 1

Answer: (D)

for a unit cube unit vector along the diagonal
$OP=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$
unit vector along the diagonal
$CD=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}-\hat{k})$
$\therefore \cos \theta =\frac{1}{3}(1+1-1)=\frac{1}{3}$
$\therefore \tan \theta =2\sqrt{2}$