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Let Q be the foot of the perpendicular drawn from the point P(a, 3, 4) to the line x - 2 1 = y + 1 2 = z - 1 -1 . If the y -coordinate of Q is 1 , then the value of a is

Options

  1. A11
  2. B-2
  3. C5
  4. D3

Correct answer

D. 3

Step-by-step solution

The equation of the given line is x - 2 1 = y + 1 2 = z - 1 -1 = . Any point on this line can be written as ( + 2, 2 - 1, - + 1) . Let the foot of the perpendicular Q have these coordinates for some value of . We are given that the y -coordinate of Q is 1 . 2 - 1 = 1 2 = 2 = 1 Substituting = 1 , the coordinates of Q are (1 + 2, 2(1) - 1, -1 + 1) = (3, 1, 0) . The direction ratios of the line segment PQ are (3 - a, 1 - 3, 0 - 4) = (3 - a, -2, -4) . The direction ratios of the given line are (1, 2, -1) . Since PQ is

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