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JEE MainMathematicsThree Dimensional Geometry

Let L' be the image of the line x-3 -1 = y+1 2 = z-1 1 in the plane 2x - y + z = 8 . If the line L' passes through the point ( , , 7) , then the value of 2 + is equal to :

Options

  1. A11
  2. B5
  3. C17
  4. D14

Correct answer

D. 14

Step-by-step solution

Let the given line be L: x-3 -1 = y+1 2 = z-1 1 = . Any general point on L is of the form (- +3, 2 -1, +1) . To find the point of intersection of L and the plane 2x - y + z = 8 , substitute this general point into the plane equation: 2(- +3) - (2 -1) + ( +1) = 8 -2 + 6 - 2 + 1 + + 1 = 8 -3 + 8 = 8 = 0 So, the point of intersection is P(3, -1, 1) . This point lies on both L and the image line L' . Now, take another point on L by setting = 1 : A(2, 1, 2) . Let A'(x', y', z') be the image of A in the plane 2x - y + z

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