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JEE Main202325 Jan 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point P 4 , 6 , - 2 from the line passing through the point - 3 , 2 , 3 and parallel to a line with direction ratios 3 , 3 , - 1 is equal to:

Options

  1. A3
  2. B6
  3. C2 3
  4. D14

Correct answer

D. 14

Step-by-step solution

The equation of line passing through the point - 3 , 2 , 3 and parallel to a line with direction ratios 3 , 3 , - 1 will be, x + 3 3 = y - 2 3 = z - 3 - 1 = λ Now let any point on the line will be, M 3 λ - 3 , 3 λ + 2 , 3 - λ We know the direction ratios of the line joining the points x 1 , y 1 , z 1 and x 2 , y 2 , z 2 is given by x 2 - x 1 , y 2 - y 1 , z 2 - z 1 Therefore, the direction ratios of line PM, D.R of PM 3 λ - 7 , 3 λ - 4 , 5 - λ Since, PM is perpendicular to the lin

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