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JEE Main201910 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

The plane which bisects the line segment joining the points - 3 , - 3 , 4 and 3 , 7 , 6 at right angles, passes through which one of the following points?

Options

  1. A2 , 1 , 3
  2. B4 , 1 , - 2
  3. C4 , - 1 , 7
  4. D- 2 , 3 , 5

Correct answer

B. 4 , 1 , - 2

Step-by-step solution

The midpoint of line joining the given points is 0 , 2 , 5 and it lies on the required plane. Normal to the plane, the line joining the given points, has direction ratio < 6 , 10 , 2 > ≡ < 3 , 5 , 1 > ⇒ equation of plane is 3 x - 0 + 5 y - 2 + z - 5 = 0 ⇒ 3 x + 5 y + z = 15 Hence plane passes through point 4 , 1 , - 2

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