JEE Mains · Maths · STD 12 - 11. three dimension geometry
The angle between the straight lines, whose direction cosines are given by the equations \(2 l+2 \mathrm{~m}-\mathrm{n}=0\) and \(\mathrm{mn}+\mathrm{n} l+l \mathrm{~m}=0\), is :
- A \(\frac{\pi}{2}\)
- B \(\pi-\cos ^{-1}\left(\frac{4}{9}\right)\)
- C \(\cos ^{-1}\left(\frac{8}{9}\right)\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{n}=2(\ell+\mathrm{m})\) \(\ell \mathrm{m}+\mathrm{n}(\ell+\mathrm{m})=0\) \(\ell \mathrm{m}+2(\ell+\mathrm{m})^{2}=0\) \(2 \ell^{2}+2 \mathrm{~m}^{2}+5 \mathrm{~m} \ell=0\) \(2\left(\frac{\ell}{\mathrm{m}}\right)^{2}+2+5\left(\frac{\ell}{\mathrm{m}}\right)=0\)…
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