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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If\[\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c},\]then\[\overrightarrow{a}(\overrightarrow{b}\times \overrightarrow{c})\]is equal to

    A)  \[\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\]

    B)  \[2\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\]

    C)  \[\overrightarrow{b}.(\overrightarrow{a}+\overrightarrow{c})\]

    D)  None of these

    Correct Answer: D

    Solution :

     Given, \[\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}\] \[\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})=(\overrightarrow{b}+\overrightarrow{c}).(\overrightarrow{b}\times \overrightarrow{c})\] \[=[\overrightarrow{b}\overrightarrow{b}\overrightarrow{c}]+[\overrightarrow{c}\overrightarrow{b}\overrightarrow{c}]=0\]


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