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JEE Main201815 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

A variable plane passes through a fixed point ( 3 , 2,1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to y z - plane through A , a second plane is drawn parallel z x plane through B and a third plane is drawn parallel to x y - plane through C . Then the locus of the point of intersection of these three planes, is

Options

  1. A(x+y+z=6)
  2. Bx 3 + y 2 + z 1 =1
  3. C3 x + 2 y + 1 z =1
  4. D1 x + 1 y + 1 z = 11 6

Correct answer

C. 3 x + 2 y + 1 z =1

Step-by-step solution

If a, b, c are the intercepts of the variable plane on the x, y, z axes respectively, then the equation of the plane is x a + y b + z c =1 And the point of intersection of the planes parallel to the x y, y z and z x planes is ( a, b , c). As the point (3,2,1) lies on the variable plane, so 3 a + 2 b + 1 c =1 Therefore, the required locus is 3 x + 2 y + 1 z =1

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