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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2015 · Mathematics · Three Dimensional Geometry

From the point P(3,-1,11) , a perpendicular is drawn on the line L...

From the point P(3,−1,11)P(3,-1,11), a perpendicular is drawn on the line LL given by the equation x2=y−23=z−34\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}. Let QQ be the foot of the perpendicular. What are the direction ratios of the line segment PQ?

Options

  1. A⟨1,6,4⟩\langle 1,6,4\rangle
  2. B⟨−1,6,−4⟩\langle-1,6,-4\rangle
  3. C⟨−1,−6,4⟩\langle-1,-6,4\rangle
  4. D⟨2,−6,4⟩\langle 2,-6,4\rangle

Correct answer

B. ⟨−1,6,−4⟩\langle-1,6,-4\rangle

Step-by-step solution

Equation of line passing through P(3,−1,11)\mathrm{P}(3,-1,11) and perpendicular to x2=y−23=z−34\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4} is: x−3−1=y−16=z−1−4\frac{x-3}{-1}=\frac{y-1}{6}=\frac{z-1}{-4} The direction ratio are (−1,6,−4)∴(-1,6,-4)\therefore \quad Option (B) is correct.
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