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JEE Main202624 January 2026Evening ShiftMathematicsVector AlgebraActual

Let a =2 i -5 j +5 k and b = i - j +3 k . If c is a vector such that 2( a c )+3( b c )= 0 and ( a - b ) c =-97 , then | c k |² is equal to

Options

  1. A233
  2. B218
  3. C193
  4. D205

Correct answer

B. 218

Step-by-step solution

2( a c ) + 3( b c ) = 0 (2 a + 3 b ) c = 0 . So c (2 a + 3 b ) = (7, -13, 19) . Let c = t(7, -13, 19) . a - b = (1, -4, 2) . ( a - b ) c = t(7 + 52 + 38) = 97t = -97 t = -1 . c = (-7, 13, -19) . c k = vmatrix i & j & k -7 & 13 & -19 0 & 0 & 1 vmatrix = (13, 7, 0) . | c k |^2 = 169 + 49 = 218 .

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