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JEE MainMathematicsVector Algebra

Let a and b be two non-collinear vectors. For all real numbers x and y , the vector v = x a + y b satisfies the relation v ( a b ) = 6(x + 2y) a - (5x + 6y) b . Then the value of | a b |^2 is equal to

Options

  1. A96
  2. B54
  3. C24
  4. D60

Correct answer

C. 24

Step-by-step solution

Given the relation: v ( a b ) = 6(x + 2y) a - (5x + 6y) b Using the Vector Triple Product expansion on the left side: v ( a b ) = ( v b ) a - ( v a ) b Substitute v = x a + y b into the dot products: v b = (x a + y b ) b = x( a b ) + y| b |^2 v a = (x a + y b ) a = x| a |^2 + y( a b ) So the left side becomes: (x( a b ) + y| b |^2) a - (x| a |^2 + y( a b )) b Equating this to the given right side: (x( a b ) + y| b |^2) a - (x| a |^2 + y( a b )) b = (6x + 12y) a - (5x + 6y) b Since a and b are non-collinear, their c

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