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JEE Main202624 January 2026Morning ShiftMathematicsVector AlgebraActual

Let a =2 i + j -2 k , b = i + j and c = a b . Let d be a vector such that | d - a |= 11 ,| c d |=3 and the angle between c and d is 4 . Then a d is equal to

Options

  1. A3
  2. B11
  3. C0
  4. D1

Correct answer

C. 0

Step-by-step solution

c = a b = vmatrix i & j & k 2 & 1 & -2 1 & 1 & 0 vmatrix = 2 i - 2 j + k | c | = 4+4+1 = 3 , | a | = 4+1+4 = 3 From | c d | = 3 and ( ( c , d )) = 1 2 : | c || d | 4 = 3 → 3| d | 1 2 = 3 → | d | = 2 From | d - a |^2 = 11 : | d |^2 - 2 a d + | a |^2 = 11 2 - 2 a d + 9 = 11 a d = 0

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