AP EAMCET201822 Apr 2018Evening ShiftMathematicsThree Dimensional GeometryActual
A(3,2,-1), B(4,1,1), C(6,2,5) and D(3,3,3) are four points. G₁, G₂, G₃ and G₄ respectively are the centroids of the triangles B C D, C D A , D A B and A B C . The point of concurrence of the lines A G₁, B G₂, C G₃ and D G₄ is
Options
- A(4, 2, 2)
- B(2, 4, 2)
- C(2, 2, 4)
- D(2, 2, 2)
Correct answer
A. (4, 2, 2)
Step-by-step solution
Given points, A(3,2,-1), B(4,1,1), C(6,2,5) and D(3,3,3) , So, G₁ is centroid of triangle BCD, G₁ ( 13 3 , 6 3 , 9 3 )G₂ is centroid of triangle CDA G₂ ( 12 3 , 7 3 , 7 3 ) The line A G₁, B G₂, C G₃ and D G₄ are concurrent, so point of concurrence of these four lines is point of intersection of lines A G₁ and B G₂ . Equation of line A G₁ is x-3 4 / 3 = y-2 0 = z+1 12 3 =r₁ (let) So, point on line this A G₁ is (3+ 4 3 r₁, 2,-1+ 12 3 r₁ ) and equation of line B G₂ is x-4 0 = y-1 4 / 3 = z-1 4 / 3 =r₂ (let) So, point