TS EAMCET · Maths · Three Dimensional Geometry
The angle between the lines whose direction cosines satisfy the equations \(l+m+n=0\), \(l^2+m^2-n^2=0\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Given, \(l+m+n=0, \quad \Rightarrow \quad l=-m-n\) and \(l^2+m^2-n^2=0\) \(\begin{aligned} & \therefore \quad(-m-n)^2+m^2-n^2=0 \\ & \Rightarrow \quad 2 m^2+2 m n=0 \\ & \Rightarrow \quad 2 m(m+n)=0 \\ & \Rightarrow \quad m=0 \text { or } m+n=0 \\ & \end{aligned}\) If \(m=0\),…
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