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MHT CET2016MathematicsThree Dimensional Geometry

If A and B are foot of perpendicular drawn from point Q a , b , c to the planes y z and z x , then equation of plane through the points A , B and O is _______

Options

  1. Ax a + y b - z c = 0
  2. Bx a - y b + z c = 0
  3. Cx a - y b - z c = 0
  4. Dx a + y b + z c = 0

Correct answer

A. x a + y b - z c = 0

Step-by-step solution

A 0 , b , c B a , 0 , c Equation of plane is x y z 1 0 b c 1 a 0 c 1 0 0 0 1 = 0 ⇒ x y z 0 b c a 0 c = 0 ⇒ b c x + c a y - a b z = 0 ⇒ x a + y b - z c = 0

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