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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The plane containing the line x - 3 2 = y - b 4 = z - 3 3 passes through the points a , 1 , 2 , 2 , 1 , 4 , 2 , 3 , 5 , then 3 a + 5 b is equal to

Options

  1. A4
  2. B16
  3. C- 16
  4. D- 4

Correct answer

C. - 16

Step-by-step solution

If the plane contains the given line then it must pass through 3 , b , 3 and should be parallel to 2 i ^ + 4 j ^ + 3 k ^ Also, the plane passes through the points a , 1 , 2 2 , 1 , 4 2 , 3 , 5 . Equation of the plane is x - 2 y - 1 z - 4 0 2 1 2 4 3 = 0 ⇒ x - 2 2 - y - 1 - 2 + z - 4 - 4 = 0 ⇒ x - 2 + y - 1 - 2 z + 8 = 0 ⇒ x + y - 2 z + 5 = 0 ∴ points 3 , b , 3 a , 1 , 2 satisfy the equation of the plane, if 3 + b - 6 + 5 = 0 ⇒ b = - 2 a + 1 - 4 + 5 = 0 ⇒ a = - 2

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