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Manipal MET2010MathematicsThree Dimensional Geometry

The reflection of the point (2,-1,3) in the plane 3 x-2 y-z=9 is

Options

  1. A( 26 7 , 15 7 , 17 7 )
  2. B( 26 7 , -15 7 , 17 7 )
  3. C( 15 7 , 26 7 , -17 7 )
  4. D( 26 7 , 17 7 , -15 7 )

Correct answer

B. ( 26 7 , -15 7 , 17 7 )

Step-by-step solution

By image formula, aligned x₂-x₁ a & = y₂-y₁ b = z₂-z₁ c & =- 2 (a x₁+b y₁+c z₁+d ) a^2+b^2+c^2 aligned aligned x₂-2 3 & = y₂+1 -2 = z₂-3 -1 & =-2 (6+2-3-9) 9+4+1 aligned array ll & x₂-2 3 = y₂+1 -2 = z₂-3 -1 = -2(-4) 14 & x₂= 26 7 , y₂= -15 7 , z₂= 17 7 array

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