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JEE Main2013MathematicsThree Dimensional GeometryActual

Let Q be the foot of perpendicular from the origin to the plane 4 x-3 y+z+13=0 and R be a point (-1,-6) on the plane. Then length Q R is :

Options

  1. A14
  2. B19 2
  3. C3 7 2
  4. D3 2

Correct answer

C. 3 7 2

Step-by-step solution

Let P be the image of O in the given plane. Equation of the plane, 4 x-3 y+z+13=0 OP is normal to the plane, therefore direction ratio of OP are proportional to 4,-3,1 Since OP passes through (0,0,0) and has direction ratio proportional to 4,-3,1 . Therefore equation of OP is aligned & x-0 4 = y-0 -3 = z-0 1 =r (let) & x=4 r, y=-3 r, z=r aligned Let the coordinate of P be (4 r,-3 r, r) Since Q be the mid point of OP Q = (2 r,- 3 2 r, r 2 ) Since Q lies in the given plane aligned & 4 x-3 y+z+13=0 & 8 r+ 9 2 r+ r 2 +

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