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JEE Main2012MathematicsThree Dimensional GeometryActual

If a = i -2 j +3 k , b =2 i +3 j - k and c =r i + j +(2 r-1 k are three vectors such that c is parallel to the plane of a and b , then r is equal to

Options

  1. A1
  2. B-1
  3. C0
  4. D2

Correct answer

C. 0

Step-by-step solution

Let a = i -2 j +3 k , and c =r i + j +(2 r-1) k Since, c is parallel to the plane of a and b therefore, a , b and c are coplanar. aligned & | array ccc 1 & -2 & 3 2 & 3 & -1 r & 1 & 2 r-1 array |=0 & 1(6 r-3+1)+2(4 r-2+r)+ & 6 r-2+10 r-4+6-9 r=0 & r=0 aligned

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