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A line L passes through the points A(1, 0, 2) and B(3, 2, 1) . If P is the point (1, 2, 3) , then the square of the perpendicular distance from P to the line L is :

Options

  1. A5
  2. B4
  3. C8
  4. D68

Correct answer

B. 4

Step-by-step solution

The direction ratios of the line L passing through A(1, 0, 2) and B(3, 2, 1) are proportional to 3-1, 2-0, 1-2 = 2, 2, -1 . The equation of the line L can be written as: x-1 2 = y-0 2 = z-2 -1 = Any general point F on the line L is given by F(2 + 1, 2 , - + 2) . If F is the foot of the perpendicular from P(1, 2, 3) to the line L , then the direction ratios of PF are: 2 + 1 - 1, 2 - 2, - + 2 - 3 = 2 , 2 - 2, - - 1 Since PF is perpendicular to the line L , the dot product of their direction ratios is zero: 2(2 ) + 2(

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