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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2024 · Mathematics · Three Dimensional Geometry

Paragraph: Let S be the line of intersection of two planes x+y+z=1...

Paragraph: Let S be the line of intersection of two planes x+y+z=1x+y+z=1 and 2x+3y−4z=82 x+3 y-4 z=8.
Question: Which of the following are the direction ratios of S ?

Options

  1. A⟨−7,−6,1⟩\langle-7,-6,1\rangle
  2. B<−7,6,1>< -7,6,1 >
  3. C⟨−6,5,1⟩\langle-6,5,1\rangle
  4. D<6,5,1>< 6,5,1 >

Correct answer

B. <−7,6,1>< -7,6,1 >

Step-by-step solution

2 planes are x+y+z=1x+y+z=1 and 2x+3y−4z=82 x+3 y-4 z=8. Let a,b,c\mathrm{a}, \mathrm{b}, \mathrm{c} are dr′s\mathrm{dr}^{\prime} \mathrm{s} is of lines of formed by intersection of planes then the lines is perpendicular to normal of both planes. a+b+c=0a+b+c=0 ....(i)  and 2a+3b−4c=0\text{ and } 2 a+3 b-4 c=0 .....(ii) a−4−3=b2+a=c3−2=λ\frac{\mathrm{a}}{-4-3}=\frac{\mathrm{b}}{2+\mathrm{a}}=\frac{\mathrm{c}}{3-2}=\lambda (Solving (i) and (ii) a=−7λ,b=6λ,c=λ\mathrm{a}=-7 \lambda, \mathrm{ b}=6 \lambda, \mathrm{c}=\lambda Dr's or ⟨−7,6,1⟩\langle-7,6,1\rangle.
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