A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{180}^{o}}\]
D) \[{{120}^{o}}\]
Correct Answer: A
Solution :
We know that, the condition when a space vector makes the angles \[\alpha ,\beta \] and \[\gamma \] with the positive direction of \[x,y\] and z-axes respectively is \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] ……(i) Given that, \[\alpha ={{150}^{o}},\beta ={{60}^{o}},\gamma =?\] From Eq. (i), \[{{\cos }^{2}}{{150}^{o}}+\beta ={{60}^{o}},co{{s}^{2}}\gamma =1\] \[(si{{n}^{2}}{{60}^{o}}+{{\cos }^{2}}{{60}^{o}})+{{\cos }^{2}}\gamma =1\] \[1+{{\cos }^{2}}\gamma =1\] \[\Rightarrow \] \[{{\cos }^{2}}\gamma =0\] \[\Rightarrow \] \[\cos \gamma =0=\cos {{90}^{o}}\] \[\Rightarrow \] \[\gamma ={{90}^{o}}\]
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