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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

A 2 , 3 , - 4 ,   B - 3 , 3 , - 2 ,   C - 1 , 4 , 2 and D 3 , 5 , 1 are the vertices of a tetrahedron. If E ,   F ,   G are the centroids of its faces containing the point A , then the centroid of the triangle E F G is

Options

  1. A1 9 , 15 9 , - 3 9
  2. B1 4 , 15 4 , - 3 4
  3. C4 9 , 11 3 , - 10 9
  4. D- 1 9 , 12 9 , 1 9

Correct answer

C. 4 9 , 11 3 , - 10 9

Step-by-step solution

Point E is the centroid of face A B C ( which is a triangle ) Centroid = x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 , z 1 + z 2 + z 3 3 E = 2 + ( - 3 ) + ( - 1 ) 3 , 3 + 3 + 4 3 , - 4 + ( - 2 ) + 2 3 E = - 2 3 , 10 3 , - 4 3 Point F is the centroid of face A C D F = 2 + ( - 1 ) + 3 3 , 3 + 4 + 5 3 , - 4 + 2 + 1 3 F = 4 3 , 12 3 , - 1 3 = 4 3 , 4 , - 1 3 Point G is the centroid of face A B D G = 2 + ( - 3 ) + 3 3 , 3 + 3 + 5 3 , - 4 + ( - 2 ) + 1 3 G = 2 3 , 11 3 , - 5 3 Now E F G form a triangle, therefore centroid of &

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