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

NDA 2015 · Mathematics · Three Dimensional Geometry

The direction ratios of the line perpendicular to the lines with...

The direction ratios of the line perpendicular to the lines with direction ratios <1,−2,−2>< 1,-2,-2 > and <0,2,1>< 0,2,1 > are

Options

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

Correct answer

A. <2,−1,2>< 2,-1,2 >

Step-by-step solution

Let the direction ratio be <a,b,c>< \mathrm{a}, \mathrm{b}, \mathrm{c} >cos⁡90∘=(a)(1)+(b)(−2)+(c)(−2)a2+b2+c2(1)2+(−2)2+(−2)2a−2b−2c=0....(1)cos⁡90∘=(a)(0)+b(2)+(c)(1)a2+b2+c2(0)2+(−2)2+(1)22b+c=0....(2)\begin{aligned} & \cos 90^{{}^{\circ}}=\frac{(a)(1)+(b)(-2)+(c)(-2)}{\sqrt{\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2} \sqrt{(1)^2+(-2)^2+(-2)^2}} \\ & \mathrm{a}-2 \mathrm{ b}-2 \mathrm{c}=0....(1) \\ & \cos 90^{{}^{\circ}}=\frac{(\mathrm{a})(0)+\mathrm{b}(2)+(\mathrm{c})(1)}{\sqrt{\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2} \sqrt{(0)^2+(-2)^2+(1)^2}} \\ & 2 \mathrm{ b}+\mathrm{c}=0....(2) \end{aligned}$Fromeq.(1)&(2)From eq. (1) \& (2)\mathrm{a}=-2 \mathrm{ b} ; \mathrm{c}=-2 \mathrm{ b}$
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