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JEE Main20238 Apr 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be the plane passing through the line x - 1 1 = y - 2 - 3 = z + 5 7 and the point ( 2 , 4 , - 3 ) . If the image of the point ( - 1 , 3 , 4 ) in the plane P is ( α , β , γ ) , then α + β + γ is equal to

Options

  1. A10
  2. B12
  3. C9
  4. D11

Correct answer

A. 10

Step-by-step solution

Given, P be the plane passing through the line x - 1 1 = y - 2 - 3 = z + 5 7 and the point ( 2 , 4 , - 3 ) , So, equation of plane is given by, x - 2 y - 4 z + 3 1 - 3 7 2 - 1 4 - 2 - 3 - - 5 = 0 ⇒ x - 2 y - 4 z + 3 1 - 3 7 1 2 2 = 0 ⇒ x - 2 - 20 - y - 4 - 5 + z + 3 5 = 0 ⇒ 4   x - y - z - 7 = 0 Now finding the image α ,   β ,   γ of the point - 1 , 3 , 4 with respect to plane 4   x - y - z - 7 = 0 we get, x + 1 4 = y - 3 - 1 = z - 4 - 1 = - 2 - 4 - 3 - 4 - 7 16

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