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JEE Main201910 Jan 2019Morning ShiftMathematicsVector AlgebraActual

Let A be a point on the line r → = 1 - 3 μ i ^ + μ - 1 j ^ + 2 + 5 μ k ^ and B 3 , 2 , 6 be a point in the space. Then the value of μ for which the vector A B → is parallel to the plane x - 4 y + 3 z = 1 is

Options

  1. A1 2
  2. B1 4
  3. C- 1 4
  4. D1 8

Correct answer

B. 1 4

Step-by-step solution

Let A is 1 - 3 μ ,   μ - 1 ,   2 + 5 μ We know that the vector joining two points x 1 ,   y 1 ,   z 1 and x 2 ,   y 2 ,   z 2 is x 2 - x 1 i ^ + y 2 - y 1 j ^ + z 2 - z 1 k ^ ⇒ A B → = 3 μ + 2 i ^ + 3 - μ j ^ + 4 - 5 μ k ^ which is parallel to plane x - 4 y + 3 z = 1 ⇒ 1 3 μ + 2 - 4 3 - μ + 3 4 - 5 μ = 0 ⇒ 3 μ + 2 - 12 + 4 μ + 12 - 15 μ = 0 ⇒   - 8 μ + 2 = 0 ⇒ μ = 1 4 .

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