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AP EAMCET201822 Apr 2018Morning ShiftMathematicsVector AlgebraActual

It a , b and c are non-coplanar vectors and the four points with position vectors 2 a +3 b - c , a -2 b +3 c , 3 a +4 b +2 c and k a -6 b +6 c are coplanar, then k=

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

Let A(2a + 3b − c), B(a − 2b + 3c) C(3a + 4b − 2c) and D(ka − 6b + 6c) ∴ AB = − a − 5b + 4c aligned & A C = a + b - c & A D =(k-2) a -9 b +7 c aligned Since, A, B, C, D are coplanar array rlrl & & | array ccc -1 & -5 & 4 1 & 1 & -1 k-2 & -9 & 7 array |=0 & & (k-2) & (5-4)+9(1-4)+7(-1+5)=0 & & k-27+28 & =0 & & k-1 & =0 & & k & =1 . array

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