JEE Mains · Maths · STD 12 - 11. three dimension geometry
The angle between the lines whose direction cosines satisfy the equations \(l + m + n = 0\) and \({l^2} = {m^2} + {n^2}\) is
- A \(\frac{\pi }{6}\)
- B \(\frac{\pi }{2}\)
- C \(\frac{\pi }{3}\)
- D \(\frac{\pi }{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi }{3}\)
Step-by-step Solution
Detailed explanation
We have, \(l + m + n = 0,{l^2} + {m^2} - {n^2} = 0.\) Eliminationg \(n\) from both the equations, we have \({l^2} + {m^2} - {\left( {l + m} \right)^2} = 0\) \( \Rightarrow {l^2} + {m^2} - {l^2} - {m^2} - 2ml = 0\) \( \Rightarrow 2lm = 0\) \( \Rightarrow lm = 0\)…
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