AP EAMCET · Maths · Three Dimensional Geometry
The acute angle between the lines whose direction cosines are given by the equations \(l+m+n=0\) and \(2 l m+2 l n-m n=0\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{2 \pi}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Given equations are, On squaring both side of the Eq. (i). \[ \begin{array}{cc} & l^2+m^2+n^2+2 l m+2 m n+2 n l=0 \\ \because & l^2+m^2+n^2=1, \end{array} \] From Eqs. (ii) and (iv), \[ 3 m n=-1 \Rightarrow m n=-\frac{1}{3} \] From Eq. (iii) \(6 l^2-1=0\), let root of this…
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