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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Let L 1 : x = y = z and L 2 : x - 1 = y - 2 = z - 3 be two lines. The foot of perpendicular drawn from the origin O 0,0 , 0 on L 1 to L 2 is A . If the equation of a plane containing the line L 1 and perpendicular to O A is 10 x + b y + c z = d , then the value of b + c + d is equal to

Options

  1. A10
  2. B- 10
  3. C12
  4. D- 7

Correct answer

B. - 10

Step-by-step solution

From diagram, O A is perpendicular to line L 2 = 0 ⇒ 1 λ + 1 + 1 λ + 2 + 1 λ + 3 = 0 ⇒ λ = - 2 So, coordinates of point A are - 1,0 , 1 O A → = - i ^ + k ^ ∵ A normal vector to required plane is O A → Equation of the required plane is - 1 x - 0 + 1 z - 0 = 0 ⇒ - x + z = 0 ⇒ 10 x - 10 z = 0 b = 0 , c = - 10 , d = 0

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