Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2021MathematicsThree Dimensional Geometry

The mid points of the sides of triangle are (1,5,-1)(0,4,-2) and (2,3,4) then centroid of the triangle

Options

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

Correct answer

B. (1,4, 1 3 )

Step-by-step solution

Given, mid points of the sides of triangle are (1,5,-1),(0,4,-2) and (2,3,4) . Let, (x₁, y₁, z₁ )=(1,5,=1) , (x₂, y₂, z₂ )=(0,4,-2) , (x₃, y₃, z₃ )=(2,3,4) . Then centroid of triangle, G(x, y, z)= aligned & ( x₁+x₂+x₃ 3 , y₁+y₂+y₃ 3 , z₁+z₂+z₃ 3 ) &G(x, y, z)= ( 1+0+2 3 , 5+4+3 3 , -1-2+4 3 ) &= (1,4, 1 3 ) aligned

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The circum radius of the triangle formed by the points (2,-1,1),(1,-3,-5) and (3,-4,-4) is 2025Let A (2,3,5), B (-1,3,2), C ( , 5, ) be the vertices of ABC . If the median through the vertex A is equally inclined to the coordinate axes, then 2025Equation of the plane passing through the origin and perpendicular to the planes x+2 y-z=1 and 3 x-4 y+z=5 is 2025If the line joining the points i +2 j and j -2 k intersects the plane passing through the points 2 i - j , 2 j +3 k and k -2 i at r , then r ( i + j + k )= 2025The vector equation of a plane passing through the line of intersection of the planes r ( i -2 k )=3, r (2 j + k )=5 and the point i +2 j +3 k is 2025The points A (-1,2,3), B (2,-3,1), C (3,1,-2) 2025The direction cosines of the line making angles 4 , 3 and (0 < < 2 ) respectively with X , Y and Z axes are 2025If the equation of the plane passing through the point (3,2,5) and perpendicular to the planes 2 x-3 y+5 z=7 and 5 x+2 y-3 z=11 is x+b y+c z+d=0 , then 2 b+3 c+d= 2025 Full Three Dimensional Geometry list All KCET PYQs