Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2010MathematicsThree Dimensional Geometry

A plane meets the coordinate axes at A, B, C so that the centroid of the triangle A B C is (1,2,4) . Then, the equation of the plane is

Options

  1. Ax+2 y+4 z=12
  2. B4 x+2 y+z=12
  3. Cx+2 y+4 z=3
  4. D4 x+2 y+z=3

Correct answer

B. 4 x+2 y+z=12

Step-by-step solution

The equation of the plane meets the coordinate axes at A, B, C is x a + y b + z c =1 (i) Let O A=a, O B=b, O C=c Also, the centroid of A B C is ( a 3 , b 3 , c 3 ) . which is equal to (1,2,4) a 3 =1 a=3 b 3 =2 b=6 c 3 =4 c=12 From Eq. (i), x 3 + y 6 + z 12 =1 or 4 x+2 y+z=12

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 AP EAMCET PYQs