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MHT CET202526 Apr 2025Evening ShiftMathematicsVector AlgebraActual

The values of x for which the angle between the vectors a =2 x^2 i +4 x j + k and b =7 i -2 j +x k is obtuse, are

Options

  1. A0 < x < 1 2
  2. B1 < x < 2
  3. C1 x 2
  4. D-1 < x < 2

Correct answer

A. 0 < x < 1 2

Step-by-step solution

Vector Angle Condition for Obtuseness The angle between vectors is obtuse when their dot product is negative. a b = (2x^2)(7) + (4x)(-2) + (1)(x) = 14x^2 - 8x + x = 14x^2 - 7x Set the inequality 14x^2 - 7x The critical points occur at x = 0 and x = 1 2 , dividing the real line into intervals. Testing values shows the inequality holds only when 0 Among the options, A matches this interval. Answer: A

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