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JEE Main2012MathematicsThree Dimensional GeometryActual

The distance of the point - i +2 j +6 k from the straight line that passes through the point 2 i +3 j -4 k and is parallel to the vector 6 i +3 j -4 k is

Options

  1. A9
  2. B8
  3. C7
  4. D10

Correct answer

C. 7

Step-by-step solution

Point is (-1,2,6) Line passes through the point (2,3,-4) parallel to vector whose direction ratios is 6,3,-4 . Equation is x-2 6 = y-3 3 = z+4 -4 = Any point on this line is given by x=6 +2, y=3 +3, z=-4 -4 Now, d. Rs of line passing through (-1,2,6) and to this line is (x+1),(y-2),(z-6) So, 6(x+1)+3(y-2)-4(z-6)=0 6 x+3 y-4 z+24=0 Now, 6(6 +2)+3(3 +3)+4(4 +4)+24=0 61 +61=0 =-1 So, x=-4, y=0, z=0 Now, distance between (-1,2,6) and (-4,0,0) is 9+4+36 = 49 =7

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