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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2006

  • question_answer
    If the area of the parallelogram with \[\vec{a}\] and \[\vec{b}\]as two adjacent sides is 15 sq unit, then the area of the parallelogram having, \[3\vec{a}+2\vec{b}\] and \[\vec{a}+3\vec{b}\] as two adjacent sides in sq unit is :

    A)  120                                       

    B)  105

    C)  75                                         

    D)  45

    Correct Answer: B

    Solution :

    We know, if a and b are two adjacent sides of a parallelogram, then Area  \[=|\vec{a}\,\times \vec{b}|=15\]  (given)...(i)  - If the sides are \[(3\,\vec{a}+2\vec{b})\] and \[(\,\vec{a}+3\vec{b}),\] then Area of parallelogram \[=|(3\vec{a}+2\vec{b})\times (\vec{a}+3\vec{b})|\] \[=|7(\vec{a}\times \vec{b})|\] \[=7|\vec{a}\times \vec{b}|\] \[=7\times 15\] (From(i))              \[=105\,sq\] unit


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