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JEE Main20236 Apr 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let the line L pass through the point ( 0 , 1 , 2 ) , intersect the line x - 1 2 = y - 2 3 = z - 3 4 and be parallel to the plane 2 x + y - 3 z = 4 . Then the distance of the point P ( 1 , – 9 , 2 ) from the line L is

Options

  1. A74
  2. B69
  3. C54
  4. D9

Correct answer

A. 74

Step-by-step solution

Given, The line L pass through the point ( 0 ,   1 ,   2 ) , intersect the line x - 1 2 = y - 2 3 = z - 3 4 and be parallel to the plane 2 x + y - 3 z = 4 , Now plotting the diagram of above data we have, Now let the direction of line which passes through 0 , 1 , 2 be a , b , c Now the line L   &   L 1 are coplanar, So coplanar condition we get, a b c 2 - 1 3 - 2 4 - 3 2 3 4 = 0 ⇒ a b c 1 1 1 2 3 4 = 0 ⇒ a - 2 b + c = 0   . . . . . . . 1 And the line L is perpendicular to th

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