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JEE Main2018MathematicsThree Dimensional GeometryActual

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

Options

  1. A3 x + 2 y + 1 z = 1
  2. B1 x + 1 y + 1 z = 11 6
  3. Cx + y + z = 6
  4. Dx 3 + y 2 + z 1 = 1

Correct answer

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

Step-by-step solution

Let plane be x a + y b + z c = 1 It passes through 3 ,     2 ,   1 . ∴ 3 a + 2 b + 1 c = 1 Now, A ( a ,   0 ,   0 ) ,   B ( 0 ,   b ,   0 ) ,   C ( 0 ,   0 ,   c ) ∴ Locus of point of intersection of planes x = a ,   y = b   &   z = c is 3 x + 2 y + 1 z = 1

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