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MHT CET202411 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

A variable plane passes through the fixed point (3,2,1) and meets X, Y and Z axes at points A , B and C respectively. A plane is drawn parallel to YZ - plane through A , a second plane is drawn parallel to ZX -plan through B, a third plane is drawn parallel to XY - plane through C . Then locus of the point of intersection of these three planes, is

Options

  1. A1 x + 1 y + 1 z = 11 6
  2. Bx 3 + y 2 + z 1 =1
  3. C3 x + 2 y + 1 z =1
  4. Dx+y+z=6

Correct answer

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

Step-by-step solution

Let the plane be x a + y b + z c =1 If passes through (3,2,1) 3 a + 2 b + 1 c =1 Now, coordinates of points A, B, C are (a, 0, 0), (0, b, 0) and (0,0, c) respectively. Equations of the planes passing through A , B , C are x= a , y= b and z = c respectively. From equation (i), we get Required locus is 3 x + 2 y + 1 z =1

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