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JEE Mains · Maths · STD 12 - 11. three dimension geometry
An angle between the lines whose direction cosines are given by the equations, \(l+ 3m + 5n\, = 0\) and \(5lm -2mn + 6nl = 0\) , is
- A \({\cos ^{ - 1}}\left( {\frac{1}{8}} \right)\)
- B \({\cos ^{ - 1}}\left( {\frac{1}{6}} \right)\)
- C \({\cos ^{ - 1}}\left( {\frac{1}{3}} \right)\)
- D \({\cos ^{ - 1}}\left( {\frac{1}{4}} \right)\)
Answer & Solution
Correct Answer
(B) \({\cos ^{ - 1}}\left( {\frac{1}{6}} \right)\)
Step-by-step Solution
Detailed explanation
Given \(l+3 m+5 n=0\) ....\((1)\) and \(5 l m-2 m n+6 n l=0\) .....\((2)\) From eq. \(( 1 )\) we have \(l=-3 m-5 n\) Put the value of \(l\) in eq. \((2),\) we get; \(5(-3 m-5 n) m-2 m n+6 n(-3 m-5 n)=0\) \(\Rightarrow 15 m^{2}+45 m n+30 n^{2}=0\)…
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