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JEE Main20257 Apr 2025Morning ShiftMathematicsVector AlgebraActual

Let the angle , 0 2 between two unit vectors a and b be ⁻¹ ( 65 9 ) . If the vector c =3 a +6 ~b +9( a b ), then the value of 9( c a )-3( c b ) is

Options

  1. A31
  2. B27
  3. C29
  4. D24

Correct answer

C. 29

Step-by-step solution

aligned & c =3 a +6 ~b +9( a b ) & ⁻¹ ( 65 9 ) = 65 9 = 4 9 & c a =3| a |^2+6 a b =3+ 6 4 9 = 51 9 & c a =3 a ~b +6| ~b |^2= 3 4 9 +6= 22 3 & 9( c a )-3( c b )=51-22=29 aligned

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