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MHT CET2011MathematicsThree Dimensional Geometry

A plane meets the axes in A, B and C such that centroid of the A B C is (1,2,3) . The equation of the plane is

Options

  1. Ax+y / 2+z / 3=1
  2. Bx / 3+y / 6+z / 9=1
  3. Cx+2 y+3 z=1
  4. DNone of the above

Correct answer

B. x / 3+y / 6+z / 9=1

Step-by-step solution

Let the plane meets the coordinate axes at A, B and C . Let O A=a, O B=b and O C=c Then, the centroid of A B C is ( a 3 , b 3 , c 3 )=(1,2,3) (given) a=3, b=6, c=9 Then, the equation of plane, meet the coordinate axes is x a + y b + z c =1 i.e. x 3 + y 6 + z 9 =1

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