KCET 2014 Math Solved Paper

Let edge of the cube is 1 unit.So, Angle between diagonals = Angle between The diagonals of the cube are OA and BC.
The DR's of diagonal OA are (1,1,1) and for BC are (−1,1,1). The angle between the diagonals is given by,
cos‌θ‌=‌

1(−1)+(1)(1)+1(1)

√12+12+12(√−12+12+12)

‌=‌

1

√3(√3)

‌=‌

1

3

θ‌=cos−1(‌

1

3

)