TS EAMCET · Maths · Three Dimensional Geometry
If the direction cosines of two lines satisfy the equations \(2 l+m-n=0\), \(l^2-2 m^2+n^2=0\) and \(\theta\) is the angle between the lines then \(\cos \theta=\)
- A \(\frac{1}{5}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{2}{3}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
\(n = 2l+m\) \(l^2 - 2m^2 + (2l+m)^2 = 0 \Rightarrow 5l^2 + 4lm - m^2 = 0\) \(5\left(\frac{l}{m}\right)^2 + 4\left(\frac{l}{m}\right) - 1 = 0 \Rightarrow \frac{l}{m} = \frac{-4 \pm \sqrt{16+20}}{10} = \frac{-4 \pm 6}{10}\) \(\frac{l_1}{m_1} = \frac{1}{5}\),…
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