JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the direction cosines of two lines satisfy the equations: \( 4l+m-n=0 \) and \( 2mn+10nl+3lm=0 \). Then the cosine of the acute angle between these lines is:
- A \( \frac{10}{\sqrt{38}} \)
- B \( \frac{20}{3\sqrt{38}} \)
- C \( \frac{10}{7\sqrt{38}} \)
- D \( \frac{10}{3\sqrt{38}} \)
Answer & Solution
Correct Answer
(D) \( \frac{10}{3\sqrt{38}} \)
Step-by-step Solution
Detailed explanation
Direction cosines of two lines satisfy the equation \(\Rightarrow 4 \ell+m-n=0\)\(\quad\)...(1) \(2 m n+10 n \ell+3 \ell m=0\)\(\quad\)...(2) & we know \(\Rightarrow \ell^2+ m ^2- n ^2=1\)\(\quad\)...(3) \(\Rightarrow n =4 \ell+ m\) putting in eqn. (1)…
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