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JEE Main202124 Feb 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point 1 , 1 , 9 from the point of intersection of the line x - 3 1 = y - 4 2 = z - 5 2 and the plane x + y + z = 17 is:

Options

  1. A19 2
  2. B2 19
  3. C38
  4. D38

Correct answer

C. 38

Step-by-step solution

Let x - 3 1 = y - 4 2 = z - 5 2 = t ⇒   x = 3 + t ,   y = 2 t + 4 ,   z = 2 t + 5 For a point of intersection with x + y + z = 17 , then it satisfies the equation of a plane. ⇒ 3 + t + 2   t + 4 + 2   t + 5 = 17 ⇒   5 t = 5 ⇒ t = 1 ⇒ The point of intersection is 4 , 6 , 7 . Then, distance between 1 , 1 , 9 and 4 , 6 , 7 is 9 + 25 + 4 = 38 .

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