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AP EAMCET202421 May 2024Morning ShiftMathematicsVector AlgebraActual

Consider the tetrahedron with the vertices A (3,2,4) , B (x₁, y₁, 0 ), C (x₂, y₂, 0 ), D (x₃, y₃, 0 ) . If the triangle BCD is formed by the lines y=x, x+y=6 and y =1 , then the centroid of the tetrahedron is

Options

  1. A( 9 4 , 7 4 , 1 )
  2. B( 11 4 , 5 4 , 1 )
  3. C(3, 7 4 , 1 )
  4. D(3,2,1)

Correct answer

C. (3, 7 4 , 1 )

Step-by-step solution

A (3,2,4), B (x₁, y₁, 0 ), C (x₂, y₂, 0 ), D (x₃, y₃, 0 ) BCD is formed by lines y=x, x+y=6, y=1 Vertices of BCD are D (1,1), C (3,3), D (5,1) Let l , m , n , p be position vectors of vertices A ; B , C , and D aligned & l =3 i +2 j +4 k , m = i + j & h =3 i +3 j , p =5 i + j aligned position vector of centroid g = l + m + n + p 4 g = 12 i +7 j +4 k 4 Co-ordinates of centroid is (3, 7 4 , 1 )

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