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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2012 · Mathematics · Three Dimensional Geometry

What are the direction ratios of the line of intersection of the...

What are the direction ratios of the line of intersection of the planes x=3z+4x=3 z+4 and y=2z−3y=2 z-3 ?

Options

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

Correct answer

C. ⟨3,2,1⟩\langle 3,2,1\rangle

Step-by-step solution

$\begin{array}{ll} & x=3 z+4 \\ \text{ and } & y=2 z-3\end{array}\Rightarrow \quad \frac{x-4}{3}=zandand\quad \frac{y+3}{2}=z\Rightarrow \quad \frac{x-4}{3}=\frac{y+3}{2}=\frac{z}{1}\thereforeDirectionratiosareproportionaltoDirection ratios are proportional to < 3,2,1 > $.
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