MHT CET · Maths · Three Dimensional Geometry
Direction cosines of the two lines are satisfied by \(l+m+n=0\) and \(2 m n+3 \ln -5 \operatorname{lm}=0\). Then the angle between these lines is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{6}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Substituting \(n = -(l+m)\) into \(2mn+3ln-5lm=0\): \(2m(-(l+m)) + 3l(-(l+m)) - 5lm = 0 \implies -2lm - 2m^2 - 3l^2 - 3lm - 5lm = 0 \implies 3l^2 + 10lm + 2m^2 = 0\)
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