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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2021 · Mathematics · Three Dimensional Geometry

If l, m, n are the direction cosines of the line x-1=2(y+3)=1-z ,...

If l,m,nl, m, n are the direction cosines of the line x−1=2(y+3)=1−zx-1=2(y+3)=1-z, then what is l4+m4+n4l^4+m^4+n^4 equal to?

Options

  1. A11
  2. B1127\frac{11}{27}
  3. C1327\frac{13}{27}
  4. D44

Correct answer

B. 1127\frac{11}{27}

Step-by-step solution

Let x−1=(y−3)=1−z−kx-1=(y-3)=1-z-k (Say) ∴l=k,m=k2\therefore l=k, m=\frac{k}{2} and n=kn=k From l2+m2+n2=1k2+(k2)2+k2=1⇒k=23\begin{aligned} & \text{ From } l^2+m^2+n^2=1 \\ & k^2+\left(\frac{k}{2}\right)^2+k^2=1 \Rightarrow k=\frac{2}{3}\end{aligned}$\begin{aligned} & \therefore l=\frac{2}{3}, m=\frac{1}{3} \text{ and } n=\frac{2}{3} \\ & \therefore l^4+m^4+n^4 \\ & =\left(\frac{2}{3}\right)^4+\left(\frac{1}{3}\right)^4+\left(\frac{2}{3}\right)^4=\frac{11}{27}\end{aligned}
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