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Manipal MET2015MathematicsThree Dimensional Geometry

The distance of the point (3,8,2) from the line x-1 2 = y-3 4 = z-2 3 measured parallel to the plane 3 x+2 y-2 z+15=0 , is

Options

  1. A2
  2. B6
  3. C9
  4. D7

Correct answer

D. 7

Step-by-step solution

Let P(3,8,2) be the given point. Let the equation of a line through P(3,8,2) and parallel to the plane 3 x+2 y-2 z+15=0 be x-3 a = y-8 b = z-2 c ...(i) Then, normal to the plane is perpendicular to the parallel line. Then, 3 a+2 b-2 c=0 Line (i) intersects the line x-1 2 = y-3 4 = z-2 3 at ...(ii) Line (i) intersects the line x-1 2 = y-3 4 = z-2 3 at Q . | array ccc 3-1 & 8-3 & 2-2 a & b & c 2 & 4 & 3 array |=0 | array lll 2 & 5 & 0 a & b & c 2 & 4 & 3 array |=0 2(3 b-4 c)-5(3 a-2 c)=0 15 a-6 b-2 c=0 (iii) On solvi

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