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MHT CET20239 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If two vertices of a triangle are A (3,1,4) and B (-4,5,-3) and the centroid of the triangle is G (-1,2,1) , then the third vertex C of the triangle is

Options

  1. A(2,0,2)
  2. B(-2,0,2)
  3. C(0,-2,2)
  4. D(2,-2,0)

Correct answer

B. (-2,0,2)

Step-by-step solution

Let a , b , c and g be the position vectors of A , B , C and G respectively. aligned & a =3 i +1 j +4 k , & b =-4 i +5 j -3 k , & g =- i +2 j + k , aligned G is centroid of ABC . array rl g & = a + b + c 3 3 g & = a + b + c 3 & 3(- i +2 j + k )=3 i + j +4 k -4 i +5 j -3 k + c c & =-3 i +6 j +3 k -3 i - j -4 k +4 i -5 j +3 k & =-2 i +0 j +2 k array Third vertex C (-2,0,2)

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