JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • 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 \[\cos \alpha =\frac{1}{\sqrt{3}}\]                    \[\therefore \,\,\,{{A}_{x}}={{A}_{y}}={{A}_{z}}=A\cos \alpha =\frac{A}{\sqrt{3}}\]

adversite


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