AP EAMCET202420 May 2024Evening ShiftMathematicsVector AlgebraActual
The angle between the diagonals of the parallelogram whose adjacent sides are 2 i +4 j -5 k , i +2 j +3 k is
Options
- A⁻¹ ( 7 69 )
- B⁻¹ ( 1 7 69 ) .
- C⁻¹ ( 1 7 )
- D⁻¹ ( 31 7 69 )
Correct answer
D. ⁻¹ ( 31 7 69 )
Step-by-step solution
We know that diagonal of parallelograms are aligned & d ₁= a + b =3 i +6 j -2 k & d ₂= a - b = i +2 j -8 k aligned Let angle between d ₁ and d ₂ is aligned & = | (3 i +6 j -2 k ) ( i +2 j -8 k ) 9+36+4 1+4+64 | & = 3+12+16 49 69 = 31 7 69 = ⁻¹ ( 31 7 69 ) aligned