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MHT CET20242 May 2024Morning ShiftMathematicsVector AlgebraActual

For all real x , the vectors C x i -6 j -3 k and x i +2 j +2 C x k make an obtuse angle with each other, then the value of C can be in

Options

  1. A(0,1)
  2. B(-2, -4 3 )
  3. C( -4 3 , 0 )
  4. D(0, 4 3 )

Correct answer

C. ( -4 3 , 0 )

Step-by-step solution

Let a =C x i -6 j -3 k and b =x i +2 j +2 C x k Angle between a and b is obtuse. array ll & a ~b 180^ & a ~b 0 & C x^2-12-6 C x 0 array aligned & C x^2-6 C x-12 0 & C 0 and D 0 & C 0 and 36 C ^2+48 C 0 & C 0 and 3 C ^2+4 C 0 & C 0, C (3 C +4) 0 & C 0,- 4 3 C 0 C & = (- 4 3 , 0 ) aligned

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