JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    If \[\vec{p}\] and \[\vec{q}\] are two diagonals of a quadrilateral such that \[|\vec{p}-\vec{q}|=\vec{p}.\vec{q},\] \[\left| {\vec{p}} \right|=1\] and \[\left| {\vec{q}} \right|=\sqrt{2},\] then the area of quadrilateral is (in sq. unit) equal to

    A) \[1/2\]               

    B)        \[1/\sqrt{2}\]                

    C) \[\sqrt{3}\]                   

    D)        \[3/2\]

    Correct Answer: A

    Solution :

    [a] \[\left| \vec{p}-\vec{q} \right|=\vec{p}.\vec{q}\] \[\Rightarrow \,\,\,\,\,\,\,{{\left| {\vec{p}} \right|}^{2}}+{{\left| {\vec{q}} \right|}^{2}}-2\vec{p}.\vec{q}=\sqrt{2}\,\,\cos \theta \] \[\Rightarrow \,\,\,\,\,\,\,\,\cos \theta =\frac{1}{\sqrt{2}}\] \[\therefore \]    Area \[=\frac{1}{2}\left| {\vec{p}} \right|.\left| {\vec{q}} \right|\,\,\,\sin \theta =\frac{1}{2}\]  

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