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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The image of the line x 2 = y - 1 5 = z + 1 3 in the plane x + y + 2 z = 3 meets the x z - plane at the point a , b , c , then the value of c is equal to

Options

  1. A11 6
  2. B129 6
  3. C115 6
  4. D232 3

Correct answer

B. 129 6

Step-by-step solution

Any general point on the line is 2 λ , 5 λ + 1,3 λ - 1 On satisfying this point on the plane, we get, 2 λ + 5 λ + 1 + 6 λ - 2 = 3 13 λ = 4 ⇒ λ = 4 13 So, coordinates of the point are 8 13 , 33 13 , - 1 13 This point also lies on the image of the line Image of point 0,1 , - 1 also lies on the image of the line x - 0 1 = y - 1 1 = z + 1 2 = - 2 - 4 6 x = 4 3 , y = 7 3 , z = 5 3 Point is 4 3 , 7 3 , 5 3 Equation of image of the line is x - 4 3 28 = y - 7 3 - 8 = z - 5 3 68

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