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JEE Main20252 Apr 2025Evening ShiftMathematicsVector AlgebraActual

Let a =2 i -3 j +k, b =3 i +2 j +5 k and a vector c be such that ( a - c ) b =-18 i -3 j +12 k and a c =3 . If b c = d , then | a d | is equal to :

Options

  1. A18
  2. B12
  3. C9
  4. D15

Correct answer

D. 15

Step-by-step solution

a =2 i -3 j + k , b =3 i +2 j +5 k a b = | array ccc i & j & k 2 & -3 & 1 3 & 2 & 5 array | aligned & =-17 i -7 j +13 k & ( a - c ) b =-18 i -3 j +12 k & ( a b )-( c b )=-18 i -3 j +12 k & b c =(-18 i -3 j +12 k )-( a b ) & =(-18 i -3 j +12 k )-(-17 i -7 j +13 k ) & b c =- i +4 j - k & a d = a ( b c )=(2 i -3 j + k ) (- i +4 j - k ) & =-2-12-1=-15 & | a d |=15 aligned

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