A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
Correct Answer: A
Solution :
\[{{\ell }^{2}}+m+n=0;\] \[{{\ell }^{2}}={{m}^{2}}+{{n}^{2}}\] \[\Rightarrow \]\[\ell =-(m+n)\] \[\Rightarrow \]\[{{m}^{2}}+{{n}^{2}}+2mn={{m}^{2}}+{{n}^{2}}\] \[\Rightarrow \]\[mn=0\]\[\Rightarrow \]\[m=0\]or\[n=0\]Case I | Case II |
\[m=0\] | \[n=0\] |
\[\ell +n=0\] | \[\ell +m=0\] |
\[\Rightarrow \]\[\ell =k\] | \[\ell =k\] |
\[m=0\] | \[m=-k\] |
\[n=-k\] | \[n=0\] |
\[\ell =1/\sqrt{2}\] | \[\ell =1/\sqrt{2}\] |
\[m=0\] | \[m=-1/\sqrt{2}\] |
\[n=-1/\sqrt{2}\] | \[n=0\] |
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