AP EAMCET · Maths · Three Dimensional Geometry
If the direction cosines of two lines are given by \(l+m+n=0\) and \(m n-2 l m-2 n l=0\), then the acute angle between those lines is
- A \(\frac{2 \pi}{5}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{60}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(l+m+n=0 \Rightarrow l=-m-n \qquad\) ...(i) \(\begin{aligned} & \text { and } m n-2 l m-2 n l=0 \\ & \Rightarrow m n+2(m+n) m+2(m+n) n=0 \\ & \Rightarrow(2 m+n)(m+2 n)=0 \Rightarrow n=-2 m \text { or } m=-2 n \\ & \Rightarrow l=m \text { or } l=n \end{aligned}\) \(\therefore\)…
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