A) \[\frac{A}{\sqrt{3}}\]
B) \[\frac{A}{\sqrt{2}}\]
C) \[\sqrt{3}\,A\]
D) \[\frac{\sqrt{3}}{A}\]
Correct Answer: A
Solution :
Let the components of \[\overrightarrow{A}\] makes angles \[\alpha ,\,\beta \]and \[\gamma \] with x, y and z axis respectively then \[\alpha =\beta =\gamma \] \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] \[\Rightarrow \]\[3{{\cos }^{2}}\alpha =1\] Þ \[\cos \alpha =\frac{1}{\sqrt{3}}\] \[\therefore \,\,\,{{A}_{x}}={{A}_{y}}={{A}_{z}}=A\cos \alpha =\frac{A}{\sqrt{3}}\]
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