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AP EAMCET202125 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Which of the following points lie on the plane passing through 2 i +3 j - k , 3 i +2 j + k and i + j +4 k ?

Options

  1. A2 i -3 j +12 k and 2 i + j + 5 2 k
  2. B2 i -3 j +13 k and 2 i + j +6 k
  3. C2 i -3 j +13 k and 2 i + 3 2 j + 5 2 k
  4. D2 i +6 k and 2 i + 3 2 j +3 k

Correct answer

C. 2 i -3 j +13 k and 2 i + 3 2 j + 5 2 k

Step-by-step solution

Let O A =2 i +3 j - k = a O B =3 i +2 j + k = b O C = i + j +4 k = c Vector equation of a plane passing through three points with position vectors a , b and c is (r − a) ×[(b − a) × (c − a)] = 0 … (i) where r =x i +y j +z k Let us find b - a =(3 i +2 j + k )-(2 i +3 j - k ) aligned & = i - j +2 k c - a & =( i + j +4 k )-(2 i +3 j - k ) & =- i -2 j +5 k ( b - a ) ( c - a ) & = | array ccr i & j & k 1 & -1 & 2 -1 & -2 & 5 array | & = i (-5+4)- j (5+2)+ k (-2-1) & =- i -7 j -3 k aligned and r - a =(x-2) i +(y-3) j +(z

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