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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    If the volume of the parallelepiped with \[\vec{a},\] \[\vec{b}\] and \[\vec{c}\]as coterminous edges is \[40\text{ }cu\]unit, then the volume   of  the   parallelepiped   having \[\vec{b}+\vec{c},\] \[\vec{c}+\vec{a}\] and \[\vec{a}+\vec{b}\] as coterminous edges in cubic unit is

    A)  \[80\]                                  

    B)  \[120\]

    C)  \[160\]                                

    D)  \[40\]

    Correct Answer: A

    Solution :

    Given,  volume of parallelepiped \[[\vec{a}\,\vec{b}\,\vec{c}]=0\]                 \[\therefore \]  Volume of parallelepiped                                            \[=[\vec{b}+\vec{c}\,\,\,\,\vec{c}+\vec{a}\,\,\,\,\,\vec{a}+\vec{b}]\]                                 \[=2[\vec{a}\,\,\vec{b}\,\,\vec{c}]\]                                 \[=2\times 40=80cu\,unit\]


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