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AP EAMCET201822 Apr 2018Evening ShiftMathematicsThree Dimensional GeometryActual

A variable plane passes through a fixed point ( , , ) and meets the coordinate axes in A, B and C . Let P₁, P₂ and P₃ be the planes passing through A, B, C and parallel to the coordinate planes Y Z, Z X, X Y respectively. Then, the locus of the point of intersection of the planes P₁, P₂ and P₃ is

Options

  1. Ax+ y+ z=1
  2. Bx + y + z =1
  3. Cx^2+ y^2+ z^2=1
  4. Dx+ y+ z=1

Correct answer

B. x + y + z =1

Step-by-step solution

Let the point A(a, 0,0), B(0, b, 0) and C(0,0, c) . So, point of intersection of planes P₁, P₂ and P₃ is P(a, b, c) Now, equation of plane A B C is plane Eq. (i) passes through the point ( , , ) , so a + b + c =1 On taking locus of point (a, b, c) we are getting, x + y + z =1

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