Question

The angle between two diagonals of a cube will be
[MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004]

• A.
  
• B.
  
• C. Variable
• D. None of these

Answer 1

The correct option is B

Let the cube be of side 'a'
O(0,0,0), D(a,a,a), B(0,a,0), G(a,0,a)
Then equation of OD and BG are $\frac{x}{a}=\frac{y}{a}=\frac{z}{a}$ and $\frac{x}{a}=\frac{y-a}{-a}=\frac{z}{a}$ respectively.

Hence, angle between OD and BG is
$co{s}^{-1}\left(\frac{a^2-a^2+a^2}{\sqrt{3a^2}.\sqrt{3a^2}}\right)=co{s}^{-1}\left(\frac{1}{3}\right)$
Note: Students should remember this question as a fact.