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JEE Main & Advanced Sample Paper JEE Main Sample Paper-34

  • question_answer
    If \[\overrightarrow{x}\] and \[\overrightarrow{y}\] be unit vectors and \[|\overrightarrow{z}|=\frac{2}{7}\] such that \[\overrightarrow{z}+(\overrightarrow{z}\times \overrightarrow{x})=\overrightarrow{y}\] and \[\theta \] is the angle between \[\overrightarrow{x}\] and \[\overrightarrow{z}\] , then the value of sin \[\theta \] is

    A)  \[\frac{1}{2}\]                                  

    B)  1

    C)  \[\frac{\sqrt{3}}{2}\]                    

    D)  \[\frac{\sqrt{3}-1}{2\sqrt{2}}\]

    Correct Answer: C

    Solution :

    \[|\vec{z}+(\vec{z}\times \vec{x}){{|}^{2}}=|\vec{y}{{|}^{2}}\,\,\Rightarrow \,|\vec{z}{{|}^{2}}+|\vec{z}{{|}^{2}}|\vec{x}{{|}^{2}}\,{{\sin }^{2}}\theta =1\] \[\Rightarrow \,|z|=\frac{1}{\sqrt{1+\,{{\sin }^{2}}\theta }}=\frac{2}{\sqrt{7}}\Rightarrow \,\sin \,\theta \,=\frac{\sqrt{3}}{2}\]


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