JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(\alpha\) be the angle between the lines whose direction cosines satisfy the equations \(l+m-n=0\) and \(l^{2}+m^{2}-n^{2}=0 .\) Then the value of \(\sin ^{4} \alpha+\cos ^{4} \alpha\) is
- A \(\frac{3}{4}\)
- B \(\frac{3}{8}\)
- C \(\frac{5}{8}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{8}\)
Step-by-step Solution
Detailed explanation
\(n =\ell+ m\) Now, \(\ell^{2}+ m ^{2}= n ^{2}=(\ell+ m )^{2}\) \(\Rightarrow 2 \ell m =0\) If \(\ell=0 \Rightarrow m = n =\pm \frac{1}{\sqrt{2}}\) And, If \(m=0 \Rightarrow n=\ell=\pm \frac{1}{\sqrt{2}}\) So, direction cosines of two lines are…
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