AP EAMCET202125 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual
The angle between any two diagonals of a cube is
Options
- A⁻¹ ( 1 3 )
- B⁻¹ ( 1 3 )
- C⁻¹ ( 1 2 )
- D⁻¹ ( 2 3 )
Correct answer
A. ⁻¹ ( 1 3 )
Step-by-step solution
Diagonal of cube O P and A Q . aligned & O P =a i +a j +a k & A Q =-a i +a j +a k aligned Angle between diagonal i.e. aligned & = -a^2+a^2+a^2 3 a^2 3 a^2 & = a^2 3 a^2 = 1 3 & = ⁻¹ ( 1 3 ) aligned