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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are the three vectors mutually perpendicular   to   each   other   and \[|\overrightarrow{a}|=1,|\overrightarrow{b}|=3\] and\[|\overrightarrow{c}|=5,\]then \[|\overrightarrow{a}-2\overrightarrow{b},\overrightarrow{b}-3\overrightarrow{c},\overrightarrow{c}-4\overrightarrow{a}|\] is equal to:

    A)  0                                            

    B)  \[-24\]

    C)  3600                     

    D)         \[-215\]

    E)  360

    Correct Answer: D

    Solution :

    \[[\overrightarrow{a}-2\overrightarrow{b},\overrightarrow{b}-3\overrightarrow{c},\overrightarrow{c}-4\overrightarrow{a}]\] \[=(\overrightarrow{a}-2\overrightarrow{b}).\{(\overrightarrow{b}-3\overrightarrow{c})\times (\overrightarrow{c}-4\overrightarrow{a})\}\] \[=(\overrightarrow{a}-2\overrightarrow{b}).\{\overrightarrow{b}\times \overrightarrow{c}-4\overrightarrow{b}\times \overrightarrow{a}+12\overrightarrow{c}\times \overrightarrow{a}\}\] \[=(\overrightarrow{a}-2\overrightarrow{b}).(\overrightarrow{a}+4\overrightarrow{c}+12\overrightarrow{b})\] \[=\overrightarrow{a}.\overrightarrow{a}-24\overrightarrow{b}.\overrightarrow{b}\] \[=1-24\times 9\] \[=1-216=-215\]


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