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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

ABC is formed by A (1,8,4), B (0,-11,4) and C(2,-3,1) . If D is the foot of the perpendicular drawn from A to BC , then the coordinates of D are

Options

  1. A(-4,5,2)
  2. B(4,-5,2)
  3. C(4,-5,-2)
  4. D(4,5,-2)

Correct answer

D. (4,5,-2)

Step-by-step solution

Let D (h, k, l) be foot of Perpendicular AD on BC . Equation of line BC is x-2 2 = y+3 8 = z-1 -3 = (say) Since equation passes through D (h, k, l) Hence h-2 2 = , k+3 8 = , l-1 -3 = h=2 +2, k=8 -3, l=-3 +1 Since AD BC Hence aligned & aligned & [(2 +2)-1] (2-0)+ [(8 -3)-8] (-3+11) &+[(-3 +1)-4] (1-4)=0 & =1 aligned aligned Hence h=4, k=5, l=-2 D (h, k, l)= D (4,5,-2)

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