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AP EAMCET2002MathematicsVector Algebra

If three points A, B and C have position vectors (1, x, 3),(3,4,7) and (y,-2,-5) respectively and if they are collinear, then (x, y) is

Options

  1. A(2,-3)
  2. B(-2,3)
  3. C(-2,-3)
  4. D(2,-3)

Correct answer

A. (2,-3)

Step-by-step solution

Given that aligned A & = i +x j +3 k , B =3 i +4 j +7 k , C & =y i -2 j -5 k A B & =2 i +(4-x) j +4 k , aligned and B C =(y-3) i -6 j -12 k Since, A, B, C are collinear, then aligned & A B =t BC & 2 i +(4-x) j +4 k =t (y-3) i -6 j -12 k & 2 i +(4-x) j +4 k =t(y-3) i -6 t j -12 t k aligned Equating the coefficient, of i , j , k aligned t(y-3) & =2, 4-x & =-6 t, and 4=-12 t t & =- 1 3 aligned aligned & 4-x=-6 (- 1 3 )=2 x=2 & and - 1 3 (y-3)=2 & y-3=-6 y=-3 & Then (x, y)=(2,-3) & aligned

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