AP EAMCET · Maths · Three Dimensional Geometry
The direction cosines of two lines are connected by the relations \(l+m-n=0\) and \(l m-2 m n+n l=0\). If \(\theta\) is the acute angle between those lines then \(\cos \theta=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{1}{\sqrt{7}}\)
- C \(\sqrt{\frac{5}{6}}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{7}}\)
Step-by-step Solution
Detailed explanation
\(\ell+m-n=0 \Rightarrow n=\ell+m \Rightarrow \ell m-2 m n+n \ell=0\) \(\Rightarrow \ell m-2 m(\ell+m)+\ell(n+m)=0\) \(\Rightarrow \ell^2-2 m^2=0 \Rightarrow \ell=-\sqrt{2} m, \ell=\sqrt{2} m\) \(\Rightarrow n=(1-\sqrt{2}) m, n=(1+\sqrt{2}) m\)…
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