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JEE MainMathematicsThree Dimensional Geometry

The point Q(3, 6, 5) is the mirror image of the point P(1, 2, 3) in a line L . If the line L intersects the z-axis at the point R(0, 0, ) , then the value of is:

Options

  1. A8
  2. B14
  3. C20
  4. D-6

Correct answer

B. 14

Step-by-step solution

The point is P(1, 2, 3) and its mirror image in the line L is Q(3, 6, 5) . The midpoint M of the line segment PQ lies on the line L and is the foot of the perpendicular from P to L . Coordinates of M = ( 1+3 2 , 2+6 2 , 3+5 2 ) = (2, 4, 4) . The line L passes through M(2, 4, 4) and R(0, 0, ) . The direction ratios of line L are proportional to the vector MR = (0-2, 0-4, -4) = (-2, -4, -4) . The line L is perpendicular to the line segment PQ . The direction ratios of PQ are proportional to the vector PQ = (3-1, 6-2,

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