AP EAMCET · Maths · Three Dimensional Geometry
If the direction cosines of two lines satisfy the equations \(l-2 \mathrm{~m}+\mathrm{n}=0\), \(l \mathrm{~m}+10 \mathrm{mn}-2 \mathrm{n} l=0\) and \(\theta\) is the angle between the lines, then \(\cos \theta=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{8}{\sqrt{70}}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{20}{3 \sqrt{70}}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{\sqrt{70}}\)
Step-by-step Solution
Detailed explanation
\(n = 2m - l\) \(lm + 10m(2m - l) - 2(2m - l)l = 0\) \(2l^2 - 13lm + 20m^2 = 0 \implies (2l - 5m)(l - 4m) = 0\) \(l_1 = 4m_1, n_1 = 2m_1 - 4m_1 = -2m_1 \implies d_1 = (4, 1, -2)\) \(l_2 = \frac{5}{2}m_2, n_2 = 2m_2 - \frac{5}{2}m_2 = -\frac{1}{2}m_2 \implies d_2 = (5, 2, -1)\)…
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