• # question_answer Vector$\overrightarrow{A}$ makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of $\overrightarrow{A}$) will be 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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