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MHT CET202013 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The foot of the perpendicular drawn from the origin to the plane x+y+3 z-4=0 is

Options

  1. A( 2 11 , 2 11 , 9 11 )
  2. B( 4 11 , 4 11 , 12 11 )
  3. C( 1 7 , 1 7 , 6 7 )
  4. D( 1 5 , 1 5 , 3 5 )

Correct answer

B. ( 4 11 , 4 11 , 12 11 )

Step-by-step solution

d.r. of er drawn from origin to the given plane are 1,1,3 . Hence equation of e r line to the plane and passing through origin is x 1 = y 1 = z 3 =K ... say Now let foot of the er be P(K, K, 3 K) Also this point P lies on given plane K + K +9 ~K -4=0 11 ~K =4 K = 4 11 Hence P ( 4 11 , 4 11 , 12 11 )

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