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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2008

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

    A)  120                                       

    B)  105

    C)  75                                         

    D)  45

    Correct Answer: B

    Solution :

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


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