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MHT CET202411 May 2024Morning ShiftMathematicsVector AlgebraActual

If a and b are two unit vectors such that 5 a +4 b and a -2 b are perpendicular to each other, then the between a and b is

Options

  1. A2 3
  2. B⁻¹ ( 2 3 )
  3. C3
  4. D⁻¹ ( 1 3 )

Correct answer

A. 2 3

Step-by-step solution

Let be the angle between a and b . Since c = a -2 ~b and d =5 a +4 ~b . are perpendicular to each other. aligned & c ~d =0 & ( a -2 ~b ) (5 a +4 ~b )=0 & 5( a a )-6( a ~b )-8( ~b ~b )=0 & 5| a |^2-6| a || b | -8| ~b |^2 & 5-6 -8=0 & =- 1 2 & = 2 3 aligned

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