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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-5

  • question_answer
    If \[\mathbf{\vec{a}}\] and \[\mathbf{\vec{b}}\] represent the diagonals of rhombus, then

    A)  \[\vec{a}.\vec{b}=0\]               

    B)  \[\vec{a}\times \vec{b}=0\]     

    C)  \[\vec{a}.\vec{b}=1\]                           

    D)  \[\vec{a}\times \vec{b}=\vec{b}\]

    Correct Answer: A

    Solution :

    [a]  \[\because \] \[\vec{a}\] and \[\vec{b}\] represent the diagonal of the rhombus, they are perpendicular to each other. \[\therefore \vec{a}.b=ab.\cos \theta \]       \[\left( \therefore \theta ={{90}^{{}^\circ }} \right)\] \[=ab.cos{{90}^{{}^\circ }}\] \[\vec{a}.\vec{b}=0\] Hence, option [a] is correct.


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