JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

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

    A)  1                    

    B)  \[\frac{1}{2}\]

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

    D)  \[\sqrt{3}\]

    Correct Answer: A

    Solution :

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

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