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JEE Main20203 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

The foot of the perpendicular drawn from the point 4 , 2 , 3 to the line joining the points 1 , - 2 , 3 and 1 , 1 , 0 lies on the plane

Options

  1. A2   x + y - z = 1
  2. Bx - y - 2   z = 1
  3. Cx - 2   y + z = 1
  4. Dx + 2   y - z = 1

Correct answer

A. 2   x + y - z = 1

Step-by-step solution

Equation of a line through given points 1 ,   - 2 ,   3 and 1 ,   1 ,   0 will be x - 1 0 = y + 2 3 = z - 3 - 3 = λ . Direction ratio of line is = 3 j ^ - 3 k ^ . A point on this line can be taken as 1 ,   3 λ - 2 ,   - 3 λ + 3 . Let this point is foot of perpendicular from point 4 ,   2 ,   3 . Direction ratio of line joining these points is = 3 i ^ + 4 - 3 λ j ^ + 3 λ k ^ . Both lines are perpendicular to each other. ⇒ Dot product of direction

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