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MHT CET202525 Apr 2025Evening ShiftMathematicsVector AlgebraActual

If is an obtuse angle between vector a and b such that | a |=5,| ~b |=3 and | a b |=5 5 then a b =

Options

  1. A10
  2. B-10
  3. C5
  4. D-5

Correct answer

B. -10

Step-by-step solution

Given: | a | = 5 , | b | = 3 , | a b | = 5 5 , with obtuse. The magnitude of the cross product yields | a b | = | a | | b | , so 5 5 = 15 . Solving gives = 5 3 . Using ^2 + ^2 = 1 , ^2 = 1 - 5 9 = 4 9 . Since is obtuse, The dot product is a b = | a | | b | = 15 (- 2 3 ) = -10 . -10

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