COMEDK · Maths · 34. Three Dimensional Geometry
The angle between the two lines whose direction cosines satisfy the relations \(l + m + n = 0\) and \(l^2 = m^2 + n^2\) is
- A \(\dfrac{\pi}{6}\)
- B \(\dfrac{\pi}{2}\)
- C \(\dfrac{\pi}{3}\)
- D \(\dfrac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Given the relations \(l + m + n = 0\) and \(l^2 = m^2 + n^2\). From the first equation, we have \(l = -(m + n)\). Substituting this into the second equation: \((-(m + n))^2 = m^2 + n^2\) \(m^2 + n^2 + 2mn = m^2 + n^2\) \(2mn = 0\) This gives either \(m = 0\) or \(n = 0\). Case…
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