The angle between any two diagonal of a cube is

• A

  $45^{\circ}$
• B

  $60^{\circ}$
• C

  $30^{\circ}$
• Correct answer
  D

  $\tan ^{-1}(2 \sqrt{2})$

Solution

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

Hence, the correct answer is option: 'D'.