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CMC Medical CMC-Medical Ludhiana Solved Paper-2008

  • question_answer
    The condition under which vectors \[(\overrightarrow{a}+\overrightarrow{b})\] and \[(\overrightarrow{a}-\overrightarrow{b})\] should be at right angles to each other is

    A)  \[\overrightarrow{a}\ne \overrightarrow{b}\]                 

    B)  \[\overrightarrow{a}\cdot \overrightarrow{b}=0\]

    C)  \[|\overrightarrow{a}|\,\,=\,\,|\overrightarrow{b}|\]                

    D)  \[\overrightarrow{a}\cdot \overrightarrow{b}=1\]

    Correct Answer: C

    Solution :

                    \[(\overrightarrow{a}+\overrightarrow{b})\cdot (\overrightarrow{a}-\overrightarrow{b})=0\] \[\Rightarrow \]               \[{{a}^{2}}-{{b}^{2}}=0\] \[\Rightarrow \]               \[|\overrightarrow{a}|\,\,=\,\,|\overrightarrow{b}|\]


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