A) \[45{}^\circ \]or \[135{}^\circ \]
B) \[60{}^\circ \]or\[90{}^\circ \]
C) \[90{}^\circ \]or\[120{}^\circ \]
D) \[60{}^\circ \]or\[120{}^\circ \]
Correct Answer: A
Solution :
The line makes an angle of\[60{}^\circ \]with the\[x-\]axis and y-axis. \[\therefore \] \[I=cos\text{ }60{}^\circ ,\text{ }m=cos\text{ }60{}^\circ \] Let the line makes an angle\[\theta \]with z-axis. \[\therefore \] \[n=cos\theta \] We know that, \[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1\] \[\Rightarrow \] \[{{(\cos 60{}^\circ )}^{2}}+{{(\cos 60{}^\circ )}^{2}}+{{n}^{2}}=1\] \[\Rightarrow \] \[{{\left( \frac{1}{2} \right)}^{2}}+{{\left( \frac{1}{2} \right)}^{2}}+{{(\cos \theta )}^{2}}=1\] \[\Rightarrow \] \[{{(\cos \theta )}^{2}}=1-\frac{1}{4}-\frac{1}{4}\] \[\Rightarrow \] \[\cos \theta =\pm \sqrt{\frac{1}{2}}\] \[\Rightarrow \] \[\cos \theta =\pm \frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[\theta =45{}^\circ \]or\[135{}^\circ \]
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