The angle between two diagonals of a cube will be
[MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004]
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 xa=ya=za and xa=y−a−a=za respectively.
Hence, angle between OD and BG is
cos−1(a2−a2+a2√3a2.√3a2)=cos−1(13)
Note: Students should remember this question as a fact.