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JEE Advanced2012MathematicsThree Dimensional GeometryActual

The point P is the intersection of the straight line joining the points Q(2,3,5) and R(1,-1,4) with the plane 5 x-4 y-z=1 . If S is the foot of the perpendicular drawn from the point T(2,1,4) to Q R , then the length of the line segment P S is

Options

  1. A1 2
  2. B2
  3. C2
  4. D2 2

Correct answer

A. 1 2

Step-by-step solution

Equation of st. line joining Q(2,3,5) and R(1,-1,4) is x-2 -1 = y-3 -4 = z-5 1 = Let P(- +2,-4 +3,- +5) Since P also lies on 5 x-4 y-z=1 -5 +10+16 -12+ -5=1 12 =8 = 2 3 P= ( 4 3 , 1 3 , 13 3 ) Now let another point S on Q R be (- +2,-4 +3,- +5) Since S is the foot of perpendicular drawn from T(2,1,4) to Q R , where dr's of S T are , 4 -2, -1 and dr's of Q R are -1,-4,-1 array ll & - -16 +8- +1=0 18 =9 = 1 2 & S= ( 3 2 , 1, 9 2 ) array Distance between P and S array l = ( 4 3 - 3 2 )²+ ( 1 3 -1 )²+ ( 13 3 - 9 2 )² =

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