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JEE Main20248 Apr 2024Morning ShiftMathematicsVector AlgebraActual

The set of all , for which the vectors a = t i +6 j -3 k and b =t i -2 j -2 t k are inclined at an obtuse angle for all t R , is

Options

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

Correct answer

C. (- 4 3 , 0 ]

Step-by-step solution

aligned & a = i +6 j -3 k & b = t i -2 j -2 k & so a b < 0, t R & t ^2-12+6 t < 0 & t ^2+6 t -12 < 0, t R & < 0 , and D < 0 & 36 ^2+48 < 0 & 12 (3 +4) < 0 & -4 3 < < 0 aligned also for a =0, a b < 0 hence a ( -4 3 , 0 ]

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