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MHT CET202415 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 angle between a and b is

Options

  1. A3
  2. B2 3
  3. C⁻¹ ( 2 3 )
  4. D⁻¹ ( 1 3 )

Correct answer

B. 2 3

Step-by-step solution

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

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