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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2017 · Mathematics · Three Dimensional Geometry

Under which one of the following conditions are the lines x=ay+b ;...

Under which one of the following conditions are the lines x=ay+b;\mathrm{x}=\mathrm{ay}+\mathrm{b} ;\mathrm{z}=\mathrm{cy}+d+\mathrm{d} and x=ey+f;\mathrm{x}=\mathrm{ey}+f ;\mathrm{z}=\mathrm{gy}+h+\mathrm{h} perpendicular?

Options

  1. Aae+cg−1=0\mathrm{ae}+\mathrm{cg}-1=0
  2. Bae+bf−1=0\mathrm{ae}+\mathrm{b} f-1=0
  3. Cae+cg+1=0\mathrm{ae}+\mathrm{cg}+1=0
  4. Dag+ce+1=0\mathrm{ag}+\mathrm{ce}+1=0

Correct answer

C. ae+cg+1=0\mathrm{ae}+\mathrm{cg}+1=0

Step-by-step solution

Given, lines x=ay+b\mathrm{x}=\mathrm{ay}+\mathrm{b} and z=cy+d\mathrm{z}=\mathrm{cy}+\mathrm{d} are perpendicular. ⇒x−ba=y1=z−dc\Rightarrow \frac{x-b}{a}=\frac{y}{1}=\frac{z-d}{c}...(i) Also, x=ey+fx=e y+f and z=gy+hz=g y+h are perpendicular. ⇒x−fe=y1=z−hg\Rightarrow \frac{\mathrm{x}-\mathrm{f}}{\mathrm{e}}=\frac{\mathrm{y}}{1}=\frac{\mathrm{z}-\mathrm{h}}{\mathrm{ g}}...(ii) We know, for ⊥r\perp^r lines a1a2+b1b2+c1c2=0⇒ae+1+cg=0a_1 a_2+b_1 b_2+c_1 c_2=0\Rightarrow \mathrm{ae}+1+\mathrm{cg}=0
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