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JEE Advanced2008MathematicsThree Dimensional GeometryActual

Paragraph: Consider the lines: L₁: x+1 3 = y+2 1 = z+1 2 , L₂: x-2 1 = y+2 2 = z-3 3 Question: The distance of the point (1,1,1) from the plane passing through the point (-1,-2,-1) and whose normal is perpendicular to both the lines L₁ and L₂ , is

Options

  1. A2 / 75
  2. B7 / 75
  3. C13 / 75
  4. D23 / 75

Correct answer

C. 13 / 75

Step-by-step solution

The equation of the plane passing through the point (-1,-2,-1) and whose normal is perpendicular to both the given lines L₁ and L₂ may be written as array rlrl (x+1)+7(y+2)-5(z+1) & =0 & x+7 y-5 z+10 & =0 array The distance of the point (1,1,1) from the plane = | 1+7-5+10 1+49+25 |= 13 75

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